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N, or n, is the fourteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is en (pronounced ), plural ens."N" Oxford English Dictionary, 2nd edition (1989); Merriam-Webster's Third New International Dictionary of the English Language, Unabridged (1993); "en," op. cit. ==History== Egyptian hieroglyph Phoenician Nun Etruscan N Greek Nu Latin N D x30px x30px x35px Latin N One of the most common hieroglyphs, snake, was used in Egyptian writing to stand for a sound like the English , because the Egyptian word for "snake" was djet. It is speculated by many that Semitic speakers working in Egypt adapted hieroglyphics to create the first alphabet, and that they used the same snake symbol to represent N, because their word for "snake" may have begun with that sound. However, the name for the letter in the Phoenician, Hebrew, Aramaic and Arabic alphabets is nun, which means "fish" in some of these languages. The sound value of the letter was —as in Greek, Etruscan, Latin and modern languages. ==Use in writing systems== represents a dental or alveolar nasal in virtually all languages that use the Latin alphabet, and in the International Phonetic Alphabet. A common digraph with is , which represents a velar nasal in a variety of languages, usually positioned word-finally in English. Often, before a velar plosive (as in ink or jungle), alone represents a velar nasal. In Italian and French, represents a palatal nasal . The Portuguese and Vietnamese spelling for this sound is , while Spanish, Breton, and a few other languages use the letter . In English, is generally silent when it is preceded by an at the end of words, as in hymn; however, it is pronounced in this combination when occurring word medially, as in hymnal. On the other hand, other consonants are often silent when they precede an at the beginning of an English word. Examples include gnome, knife, mnemonic, and pneumonia. is the sixth-most common letter and the second-most commonly used consonant in the English language (after ). ==Other uses== In mathematics, the italic form n is a particularly common symbol for a variable quantity which represents a natural number. The set of natural numbers is referred to as \mathbb{N}. ==Related characters== ===Descendants and related characters in the Latin alphabet=== *N with diacritics: Ń ń Ñ ñ Ň ň Ǹ ǹ Ṅ ṅ Ṇ ṇ Ņ ņ Ṉ ṉ Ṋ ṋ Ꞥ ꞥ ᵰ ᶇ *Phonetic alphabet symbols related to N (the International Phonetic Alphabet only uses lowercase, but uppercase forms are used in some other writing systems): **Ŋ ŋ : Latin letter eng, which represents a velar nasal in the IPA **𝼔 : Small letter eng with palatal hook, which is used in phonetic transcription **𝼇 : Small letter reversed eng, which is an extension to IPA for disordered speech (extIPA) **Ɲ ɲ : Latin letter Ɲ, which represents a palatal nasal or an alveolo-palatal nasal in the IPA **n : Superscript small n, which represents a nasal release in the IPA **Ƞ ƞ : Latin letter Ƞ (encoded in Unicode as "N with long right leg"), a mostly obsolete letter used to transcribe various nasal sounds ** ɳ : Latin letter n with a hook, which represents a retroflex nasal in the IPA ** ᶯ : Modifier letter small n with retroflex hook ** ᶮ : Modifier letter small n with left hook **ɴ : Small capital N, which represents a uvular nasal in the IPA **ᶰ : Modifier letter small capital N *Uralic Phonetic Alphabet-specific symbols related to N: ** ** ** ** *n : Subscript small n was used in the Uralic Phonetic Alphabet prior to its formal standardization in 1902 * Teuthonista phonetic transcription system uses and * ȵ : N with curl is used in Sino-Tibetanist linguistics *Ꞑ ꞑ : N with descender *: Small letter n with mid-height left hook was used by the British and Foreign Bible Society in the early 20th century for romanization of the Malayalam language. ===Ancestors and siblings in other alphabets=== *𐤍 : Semitic letter Nun, from which the following symbols originally derive **Ν ν : Greek letter Nu, from which the following symbols originally derive *** : Coptic letter Ne ***Н н : Cyrillic letter En *** 𐌍 : Old Italic N, which is the ancestor of modern Latin N *** : Gothic letter nauþs ===Derived signs, symbols and abbreviations=== *₦ : Nigerian Naira ==Computing codes== : 1 ==Other representations== ==References== ==External links== * * Category:ISO basic Latin letters
N was a streetcar line in Los Angeles, California. It was operated by the Los Angeles Railway from 1920 to 1950. The line ran from Spring and 2nd Streets to 8th Street and Western Avenue, by way of Spring Street, 9th Street, Vermont Avenue, and 8th Street. ==History== The Ninth Street Line was built by the Los Angeles Railway in 1895 and ran via Spring Street, 9th Street, and Park View to a junction with the Lincoln Heights Line at 10th and Hoover Streets. From there both routes ran along West 10th Street to a terminus at Vermont Avenue. Circa 1911, the Park View section was eliminated and the route was extended along 9th Street, Vermont, and 8th Street to a loop at Western Avenue. In 1920, the line was rerouted, operating from 8th and Harvard via 8th; Vermont; 9th; Spring; 2nd; Traction Way; 3rd; and Santa Fe to 2nd, terminating at the Los Angeles Atchison, Topeka and Santa Fe Railway station. It was given the letter designation N in 1921. Tracks were laid on a newly-rebuilt Spring Street in June 1932, extending the line to the Sunset Boulevard Plaza. Cars were temporarily routed to Union Station as the line's northern terminal between May 1939 and June 1946. In 1950 the route was removed, though the 8th Street section of the line continued to run as part of the re-routed S line. ==Sources== ==External links== * N Line Archives — Pacific Electric Railway Historical Society * Category:Los Angeles Railway routes Category:Railway services introduced in 1905 Category:1905 establishments in California Category:Railway services discontinued in 1950 Category:1950 disestablishments in California
The N Broadway Express is a rapid transit service in the B Division of the New York City Subway. Its route emblem, or "bullet," is colored , since it uses the BMT Broadway Line in Manhattan. The N operates at all times between Ditmars Boulevard in Astoria, Queens, and Stillwell Avenue in Coney Island, Brooklyn, via the BMT Astoria Line in Queens, Broadway Line in Manhattan, the south side of the Manhattan Bridge, and the BMT Fourth Avenue and Sea Beach Lines in Brooklyn. North of 57th Street, limited rush hour service operates via the Second Avenue Subway, originating and terminating at 96th Street on the Upper East Side of Manhattan instead of Ditmars Boulevard. During the daytime on weekdays, the N runs express between 34th Street–Herald Square in Manhattan and 59th Street in Brooklyn and local elsewhere. Local service in Manhattan is provided by the R and W, which is internally staffed and scheduled as part of the N. Select rush-hour N trains in the reverse-peak direction provide regular express service in Manhattan but stop at DeKalb Avenue and operate local on the Fourth Avenue Line in Brooklyn. Weekend daytime service is the same as weekday service, except that the N makes all stops in Manhattan between Herald Square and Canal Street. During late nights, the N makes all stops along its entire route and uses the Montague Street Tunnel to travel between Manhattan and Brooklyn. The N was originally the Brooklyn–Manhattan Transit Corporation's 4 service, running along the BMT Sea Beach Line to the Manhattan Bridge. The 4 used the BMT Nassau Street Line in Lower Manhattan from 1915 to 1917, after which it ran express on the BMT Broadway Line. The 4 became the N in 1961. The N ran local in Queens along the IND Queens Boulevard Line to Forest Hills–71st Avenue from 1976 until 1987, when it switched terminals with the R. From 1986 to 2004, reconstruction on the Manhattan Bridge forced the N to run local on the Broadway Line via the Montague Street Tunnel. == Service history == 90px Original designation for the Sea Beach Line ===Before 1970=== 90px 1967–1979 bullet 90px NX bullet, used in 1967–1968 90px Diamond N bullet, used in 1979–1986 to note local service to Whitehall Street The route that is now the N was originally BMT service 4, known as the Sea Beach Line or Sea Beach Express. On June 22, 1915, the current BMT Sea Beach Line opened, replacing a street level "el" that branched off of the Fifth Avenue El with the former BMT West End Line. Originally, it used the south tracks of the Manhattan Bridge, which at that time connected to the BMT Nassau Street Line. Trains began running express between Pacific Street and 59th Street with the extension of the Fourth Avenue Line to 86th Street. On September 4, 1917, the first part of the BMT Broadway Line and the north side tracks of the Manhattan Bridge opened. Trains ran from 14th Street–Union Square to Coney Island–Stillwell Avenue, now using the bridge's northern tracks. On January 15, 1918, service was extended to Times Square–42nd Street. Weekday and Saturday summer trains leaving Coney Island between 6:37 a.m. and 8:37 p.m. began running non-stop between Kings Highway and 59th Street on August 1, 1920. Trains that started at Kings Highway made local stops. On November 14, 1920, weekday rush hour trains, and Saturday AM rush hour trains began skipping Myrtle Avenue and DeKalb Avenue. Between 1924 and 1926, trains skipped Myrtle Avenue and DeKalb Avenue during weekday rush hours, and on Saturday southbound between 12:01 p.m. and 6:57 p.m. Between 4:30 p.m. and 7:30 p.m. weekdays, and 12:01 p.m. to 6:57 p.m. Southbound on Saturdays, the rear two cars at Canal Street were restricted to boarding only (no exiting the train). In June 1931, trains skipped Myrtle Avenue and DeKalb Avenue between 7 a.m. and 12:30 a.m. weekdays, and between 10:30 a.m. Sunday to 12:30 a.m. Monday. Trains skipped 36th Street during the morning rush hour in the northbound direction. Between 1933 and 1937, the hours in which trains skipped Myrtle Avenue and DeKalb Avenue were 7 a.m. and 12:00 a.m. weekdays. On June 29, 1950, trains began running express in Brooklyn during late nights. As of June 28, 1951, every other morning rush hour train no longer terminated at Kings Highway. On May 2, 1957, service was extended north via the express tracks from Times Square to 57th Street–Seventh Avenue, and trains stopped bypassing 36th Street during the AM rush hour. In fall 1959, trains began stopping at DeKalb Avenue during midday hours. Previously, they bypassed DeKalb Avenue at all times except late nights. Beginning on January 1, 1961, trains bypassed DeKalb Avenue during rush hours only. In addition, on weekday and Saturday evenings, late nights, and all day Sundays, they ran local on the BMT Fourth Avenue Line. The N designation began to appear when R27 subway cars were moved to the service in April 1961. thumb|Poster advertising a new NX service thumb|Poster advertising the NX service's discontinuation The NX designation was used for a rush hour peak-direction "super-express" service along the express tracks of the Sea Beach Line, beginning in the AM rush hour at Brighton Beach on the BMT Brighton Line, running through Coney Island, and then following the N route to 57th Street–Seventh Avenue. (Reverse in the PM rush hour.) This short-lived service began on November 27, 1967 (with the opening of the Chrystie Street Connection)service notice, effective November 27, 1967. Archived from the original on September 24, 2020. and ended April 12, 1968, due to low ridership. Starting on Monday, April 15, 1968, the five NX trips instead ran as N trips.service notice, effective April 15, 1968. Archived from the original on November 20, 2019. On December 31, 1972, all late night trains began running local in Brooklyn. Late weekday evening trains, weekend southbound trains, and northbound early weekday trains began stopping at 53rd Street and 45th Street. ===1970–1980=== On August 30, 1976, weekday N service was extended north over the BMT 60th Street Tunnel Connection to Forest Hills–71st Avenue to replace the discontinued EE. While many N trains ran the full route from Coney Island to 71st Avenue, via the Manhattan Bridge and Broadway Express, some trains ran local during the rush hours only (southbound in the AM rush hour, and northbound in the PM rush hour) between Whitehall Street–South Ferry in Lower Manhattan and Forest Hills–71st Avenue, which had been the former EE route; these trains were noted with diamond N bullets from 1979. Trains stopped terminating at Kings Highway in the AM rush hour. On January 24, 1977, as part of a series of NYCTA service cuts to save $13 million, many subway lines began running shorter trains during middays. As part of the change, N trains began running with four cars between 9:30 a.m. and 2:15 p.m. On August 27, 1977, N service was cut back during late nights, only operating between 36th Street and Coney Island. Northbound trains ran express between 59th Street and 36th Street while southbound trains ran local. ===1980–1990=== On November 26, 1984, evening rush hour trains that terminated at Kings Highway were extended to Coney Island. Reconstruction of the Manhattan Bridge between 1986 and 2004 disrupted N service, usually rerouting it via the Montague Street Tunnel. On April 26, 1986, the north side tracks (leading to the IND Sixth Avenue Line) were closed and services that normally ran on them were moved to the south side, running via the BMT Broadway Line. Because of the large amount of train traffic now running on those tracks, rush hour and midday N service was rerouted via the Montague Street Tunnel, making local stops in Manhattan and Brooklyn, though evening, night and weekend trains continued to use the bridge and express tracks in Brooklyn. Late evening trains that ran via the bridge also ran local in Brooklyn heading southbound. Six trains only ran between Continental Avenue and Whitehall Street in the AM rush hour, while six trains only ran between Canal Street and Continental Avenue in the PM rush hour. The , which was rerouted from the BMT Brighton Line to the BMT West End Line, replaced the N as the weekday express on the Fourth Avenue Line. Starting on April 28, 1986, one Q train ran to Continental Avenue at 7:05 a.m., and returned in service as an N train, and an N train arriving at Continental Avenue at 3:25 p.m. began returning in service as a B train. These special B and Q trips no longer ran after May 23, 1987. As part of the New York City Transit Authority's proposed service plan to serve the new Archer Avenue Line upper level, the N would have been extended to Jamaica Center during weekdays. When N trains terminated at 71st Avenue or 57th Street–Seventh Avenue during weekends and evenings, G trains would have been extended to Jamaica Center, and during late nights a G train shuttle would have run between Jamaica Center and Van Wyck Boulevard. This service plan would have allowed E and F trains to remain on the Queens Boulevard mainline toward 179th Street. The final service plan, which took effect on December 11, 1988, had the extension served by E trains, with R trains extended to 179th Street. On May 24, 1987, the N swapped northern terminals with the . The N was switched to Astoria–Ditmars Boulevard, while the went to Forest Hills–71st Avenue. This was done to give the R direct access to Jamaica Yard; previously, the N had direct access to both Jamaica Yard and Coney Island Yard, and the R, running from Bay Ridge to Astoria, lacked direct access to any yard. This change was intended to improve the appearance and reliability of service on the R, since all trains on the Astoria and Broadway Lines were part of the graffiti-free program. Trains ran via the Manhattan Bridge during late nights and weekends. Some trains began went into service at 86th Street during the AM rush hour put-ins. Between November 23, 1987, and May 13, 1988, one D train arrived at Ditmars Boulevard at 7:12 a.m. and returned in service as an N train. When the north side of the Manhattan Bridge reopened and the south side was closed on December 11, 1988, the N began running local in Manhattan and via the Montague Tunnel at all times. In order to replace B service to Ditmars Boulevard, additional N service was provided during rush hours. Trains continued to run express in Brooklyn between Pacific Street and 59th Street/Fourth Avenue evenings and weekends. On June 11, 1990, trains that were put into service at Queensboro Plaza in the PM rush hour were discontinued. Between June 10, 1990, and July 25, 1992, due to construction work in the 60th Street Tunnel, trains had to use a single track. Trains operated either between Ditmars Boulevard and Canal Street, or between 57th Street and Coney Island. The Transit Authority and politicians pressured the New York State Department of Transportation to resume N train service on the bridge's south side on September 30, 1990, despite warnings from engineers that the structure was unsafe and major repairs still had to be made. Trains ran express on Broadway in Manhattan (stopping at 49th Street) and Fourth Avenue in Brooklyn at all times except late nights (10 p.m. to 5 a.m.). Southbound Brooklyn expresses ran until late evenings on Saturday, not running on Sunday morning any more. Between early morning and early evenings, trains skipped DeKalb Avenue. Several trains after the AM rush hour went out of service at Kings Highway. On December 27, state inspectors forced N service to be rerouted via the Montague Street Tunnel again after discovery of corroded support beams and missing steel plates, running local on its entire route at all times. ===1990–2000=== In November 1993, before the Manhattan Bridge's renovation was completed, the MTA proposed restoring express N service along the Fourth Avenue Line for a six-month trial period, with the M making local stops between Pacific Street and 36th Street. Some residents of Sunset Park, Brooklyn, opposed the proposal, which they claimed would negatively impact about 7,000 daily riders at the 45th Street and 53rd Street stations. On May 31, 1994, the N began running express in Brooklyn between Pacific Street and 59th Street–Fourth Avenue during weekday midday and rush hours, with the M running local during those times. From 1994 to May 22, 1995, the southern terminal of the N was 86th Street due to rehabilitation work at Coney Island–Stillwell Avenue. On November 4, 2001, it was cut back again as the terminal's reconstruction project continued. From April 30, 1995, to November 12, 1995, the north side of the Manhattan Bridge was closed during weekday midday and weekends for structural repairs. Midday N service ran local in Brooklyn, replacing the M, which was cut back from 9th Avenue to Chambers Street. The N continued to run express during rush hours. ===2001–2010=== After the September 11, 2001, attacks, Broadway Line service through Lower Manhattan was suspended; N service was also suspended and replaced by the in Manhattan and Queens and the in Brooklyn. On October 28, N service was restored, but Cortlandt Street remained closed until September 15, 2002. On September 8, 2002, because of the ongoing reconstruction of Coney Island terminal, weekend and late night N service was reduced to a shuttle between 86th and Pacific Streets, running express on the BMT Fourth Avenue Line. In its place, the was extended to Manhattan and Astoria, Queens at all times; this was because the W was the only route still serving Stillwell Avenue during this part of the reconstruction. On February 22, 2004, the Manhattan Bridge work was finally completed. The N returned to its full route in Manhattan and Queens at all times, and returned to using the Manhattan Bridge at all times except nights (via Fourth Avenue express, bypassing DeKalb Avenue). On weekdays, N trains ran express between 34th Street in Manhattan and 59th Street/Fourth Avenue in Brooklyn via the Manhattan Bridge, and local elsewhere; several trains ran express on the entire Broadway Line and short- turned at 57th Street–Seventh Avenue or Times Square during the morning rush hour. On weekends, it made local stops in Manhattan, but ran express in Brooklyn, using the Bridge. During late nights, it ran local along its entire route via the Montague Street Tunnel, replacing the train. On May 29, 2005, the new Stillwell Avenue terminal was completed, and N service between 86th Street and Coney Island was restored. On June 28, 2010, the N began running local in Manhattan north of Canal Street at all times, replacing the on weekdays which was discontinued due to budget problems, effectively adopting the weekend service pattern. However, the handful of short-turn N trains continued to run express in Manhattan. ===2011–present=== From August 2, 2013, to September 14, 2014, the Montague Street Tunnel was closed for Hurricane Sandy-related repairs. During this time, overnight N service was rerouted via the Manhattan Bridge, skipping six stations it normally served. On November 7, 2016, the MTA restored the BMT Broadway Line services to their 2004–2010 service pattern in preparation for the rerouting of the train to the Second Avenue Subway. As a result, the N train once again became a weekday express between 34th Street–Herald Square and Canal Street, with local service replaced by the restored W train.* * The MTA approved the service change on May 23, 2016. All short-turn N trains that originally terminated at 57th Street–Seventh Avenue were extended to 96th Street–Second Avenue on January 3, 2017, following the opening of the Second Avenue Subway. In January 2017, the MTA revealed plans to rehabilitate the tunnel structure above the BMT Fourth Avenue Line's express tracks between 36th Street and 59th Street. As a result, from July 30, 2018, to July 29, 2019, N trains ran local along that section at all times. Between October 21, 2019, and May 4, 2020, N trains terminated at 86th Street so work could be completed to protect Coney Island Yard from flooding. An out-of-system transfer was available between the N at 86th Street and the F at Avenue X station. The N began running local in Manhattan in March 2020 after the W was temporarily suspended due to the COVID-19 pandemic; regular N and W service was restored in June. In May 2020, the N began operating local along Fourth Avenue on most weekends to provide a transfer to the F at Fourth Avenue–Ninth Street, since the F was suspended south of Church Avenue due to construction on the IND Culver Line. In 2021, the northbound trips to 96th Street-Second Avenue were officially reclassified as Q trains via Sea Beach; the southbound trips from 96th Street-Second Avenue remained unchanged. == Route == === Service pattern === The following table shows the lines used by the N, with shaded boxes indicating the route at the specified times: Line From To Tracks Times Times Times Times Line From To Tracks rush hours week­days week­ends late nights IND Second Avenue Line 96th Street 72nd Street all Limited service BMT 63rd Street Line (full line) Lexington Avenue–63rd Street Lexington Avenue–63rd Street all Limited service BMT Astoria Line (full line) Astoria–Ditmars Boulevard Queensboro Plaza local Most trains 60th Street Tunnel 60th Street Tunnel 60th Street Tunnel all Most trains BMT Broadway Line (full line) Lexington Avenue/59th Street Times Square–42nd Street local Most trains BMT Broadway Line (full line) 57th Street–Seventh Avenue Times Square–42nd Street express Limited service BMT Broadway Line (full line) 34th Street–Herald Square Canal Street express BMT Broadway Line (full line) 34th Street–Herald Square Canal Street local BMT Broadway Line (full line) City Hall Whitehall Street–South Ferry all Most trains Manhattan Bridge Manhattan Bridge Manhattan Bridge south Very limited service Montague Street Tunnel Montague Street Tunnel Montague Street Tunnel all Most trains BMT Fourth Avenue Line Court Street Jay Street–MetroTech all Most trains BMT Fourth Avenue Line DeKalb Avenue DeKalb Avenue tunnel Limited service BMT Fourth Avenue Line DeKalb Avenue DeKalb Avenue bypass Most trains BMT Fourth Avenue Line Atlantic Avenue–Barclays Center 59th Street/Fourth Avenue express Most trains BMT Fourth Avenue Line Atlantic Avenue–Barclays Center 59th Street/Fourth Avenue local Limited service BMT Sea Beach Line (full line) Eighth Avenue Coney Island–Stillwell Avenue local === Stations === For a more detailed station listing, see the articles on the lines listed above. 20px|N service to Astoria/Ditmars Boulevard 20px|N service to Astoria/Ditmars Boulevard 20px|N service to 96th Street Stations Subway transfers Connections and notes Manhattan Manhattan Manhattan Manhattan Manhattan Manhattan Manhattan Second Avenue Line (limited rush hour service only) Second Avenue Line (limited rush hour service only) Second Avenue Line (limited rush hour service only) Second Avenue Line (limited rush hour service only) Second Avenue Line (limited rush hour service only) Second Avenue Line (limited rush hour service only) Second Avenue Line (limited rush hour service only) align=center rowspan=3 colspan=2 ↓ M15 Select Bus Service ↓ M15 Select Bus Service M86 Select Bus Service ↓ M15 Select Bus Service 63rd Street Line (limited rush hour service only) 63rd Street Line (limited rush hour service only) 63rd Street Line (limited rush hour service only) 63rd Street Line (limited rush hour service only) 63rd Street Line (limited rush hour service only) 63rd Street Line (limited rush hour service only) 63rd Street Line (limited rush hour service only) align=center colspan=2 ↓ Out-of-system transfers with MetroCard/OMNY: (IRT Lexington Avenue Line at ) (BMT Broadway Line at ) Queens Queens Queens Queens Queens Queens Queens Astoria Line Astoria Line Astoria Line Astoria Line Astoria Line Astoria Line Astoria Line align=center rowspan=7 M60 Select Bus Service to LaGuardia Airport Columbia Transportation: Queens-Riverdale Commuter Route (IRT Flushing Line) Manhattan Manhattan Manhattan Manhattan Manhattan Manhattan Manhattan Broadway Line Broadway Line Broadway Line Broadway Line Broadway Line Broadway Line Broadway Line align=center rowspan=2 (IRT Lexington Avenue Line at ) Out-of-system transfer with MetroCard/OMNY: (63rd Street Lines at ) Roosevelt Island Tramway Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Services to 96th Street (Manhattan) and Astoria–Ditmars Boulevard (Queens) split Broadway Line (Astoria and Second Avenue branches merge) Broadway Line (Astoria and Second Avenue branches merge) Broadway Line (Astoria and Second Avenue branches merge) Broadway Line (Astoria and Second Avenue branches merge) Broadway Line (Astoria and Second Avenue branches merge) Broadway Line (Astoria and Second Avenue branches merge) Broadway Line (Astoria and Second Avenue branches merge) ↓ | ↑ Station is ADA-accessible in the northbound direction only. ↓ (IRT Broadway–Seventh Avenue Line) (IRT Flushing Line) (IND Eighth Avenue Line at ) (42nd Street Shuttle) (IND Sixth Avenue Line at , daytime only) Port Authority Bus Terminal M34A Select Bus Service ↓ (IND Sixth Avenue Line) M34 / M34A Select Bus Service PATH at Amtrak, LIRR, NJ Transit at Pennsylvania Station | | M23 Select Bus Service ↓ (BMT Canarsie Line) (IRT Lexington Avenue Line) M14A / M14D Select Bus Service | | Manhattan Bridge branch Manhattan Bridge branch Manhattan Bridge branch Manhattan Bridge branch Manhattan Bridge branch Manhattan Bridge branch Manhattan Bridge branch ↓ 20px|alt=Elevator access to mezzanine only (IRT Lexington Avenue Line) (BMT Nassau Street Line) Stops on the lower level, under Canal Street. Lower Manhattan branch (night service only) Lower Manhattan branch (night service only) Lower Manhattan branch (night service only) Lower Manhattan branch (night service only) Lower Manhattan branch (night service only) Lower Manhattan branch (night service only) Lower Manhattan branch (night service only) align=center rowspan=5 20px|alt=Elevator access to mezzanine only (IRT Lexington Avenue Line) (BMT Nassau Street Line) Stops on the upper level, under Broadway. (IRT Broadway–Seventh Avenue Line at ) (IND Eighth Avenue Line at ) (IND Eighth Avenue Line at ) PATH at 20px|alt=Elevator access to mezzanine only (IRT Broadway–Seventh Avenue Line at ) Staten Island Ferry at Whitehall Terminal Brooklyn Brooklyn Brooklyn Brooklyn Brooklyn Brooklyn Brooklyn Montague Street branch Montague Street branch Montague Street branch Montague Street branch Montague Street branch Montague Street branch Montague Street branch align=center rowspan=2 20px|alt=Elevator access to mezzanine only (IRT Broadway–Seventh Avenue Line at ) (IRT Eastern Parkway Line at ) (IND Fulton Street and Culver Lines) Fourth Avenue Line (tunnel and bridge branches merge) Fourth Avenue Line (tunnel and bridge branches merge) Fourth Avenue Line (tunnel and bridge branches merge) Fourth Avenue Line (tunnel and bridge branches merge) Fourth Avenue Line (tunnel and bridge branches merge) Fourth Avenue Line (tunnel and bridge branches merge) Fourth Avenue Line (tunnel and bridge branches merge) | ↓ (BMT Brighton Line) (IRT Eastern Parkway Line) LIRR Atlantic Branch at Atlantic Terminal | | (IND Culver Line at ) | | ↓ | | ↓ Sea Beach Line Sea Beach Line Sea Beach Line Sea Beach Line Sea Beach Line Sea Beach Line Sea Beach Line ↓ ↑ Station is ADA-accessible in the northbound direction only. ↓ ↓ (BMT West End Line at ) ↓ ↓ ↓ ↓ B82 Select Bus Service ↓ ↓ Southern terminal for select rush-hour trains ↓ (BMT West End Line) (IND Culver Line) (BMT Brighton Line) == Notes == == References == == External links == * MTA NYC Transit – N Broadway Express * * # Category:New York City Subway services
N is the fifth full-length studio album by Finnish melodic death metal band Norther. The album was released through Century Media Records on 13 February 2008 in Finland, and other dates in February for other parts of Europe. The track "Frozen Angel" from their previous EP, No Way Back, was re-recorded for the album. "We Rock" and "Frozen Angel" have been made into music videos. This is also the last Norther album to have founding member Petri Lindroos on vocal and guitar duties. == Track listing == All songs written by Kristian Ranta, except where noted. == Credits == === Band members === * Petri Lindroos − lead vocals, guitar * Kristian Ranta − guitar, vocals (on 1,2,4,7,10,15) * Heikki Saari − drums * Jukka Koskinen − bass and Death growl * Tuomas Planman − keyboards, programming === Production === * Recorded and produced by Anssi Kippo at Astia Studios. * Mixed by Fredrik Nordström at Studio Fredman in Sweden. == Release history == Region Date Finland 13 February 2008 Austria 22 February 2008 Belgium Germany Italy Luxembourg Netherlands Switzerland Denmark 25 February 2008 France Greece Norway United Kingdom Portugal 26 February 2008 Spain Hungary 29 February 2008 Sweden == References == Category:2008 albums Category:Norther albums Category:Century Media Records albums
ん, in hiragana or ン in katakana, is one of the Japanese kana, which each represent one mora. ん is the only kana that does not end in a vowel sound (although in certain cases the vowel ending of kana, such as す, is unpronounced). The kana for mu, む/ム, was originally used for the n sound as well, while ん was originally a hentaigana used for both n and mu. In the 1900 Japanese script reforms, hentaigana were officially declared obsolete and ん was officially declared a kana to represent the n sound. In addition to being the only kana not ending with a vowel sound, it is also the only kana that does not begin any words in standard Japanese (other than foreign loan words such as "Ngorongoro", which is transcribed as ンゴロンゴロ) (see Shiritori). Some regional dialects of Japanese feature words beginning with ん, as do the Ryukyuan languages (which are usually written in the Japanese writing system), in which words starting with ン are common, such as the Okinawan word for miso, nnsu (transcribed as ンース). In the Ainu language, ン is interchangeable with the small katakana ㇴ as a final n. The kana is followed by an apostrophe in some systems of transliteration whenever it precedes a vowel or a y- kana, so as to prevent confusion with other kana. However, like every other kana besides yōon, it represents an entire mora, so its pronunciation is, in practice, as close to "nn" as "n". The pronunciation can also change depending on what sounds surround it. These are a few of the ways it can change: * (before n, t, d, r, ts, z, ch and j ) * (before m, p and b ) * (before k and g) * (at the end of utterances) * (before vowels, palatal approximants (y), consonants h, f, s, sh and w) * (after the vowel i if another vowel, palatal approximant or consonant f, s, sh, h or w follows.) Form Rōmaji Hiragana Katakana Normal n (ん) n ん ン nn n̄ んん んー ンン ンー Other additional forms {|align="center" style="background: transparent" Rōmaji Hiragana Katakana nwa んわ ンワ Nwankwo Kanu (ンワンクウォ・カヌ Nwankuwo Kanu) nwi んうぃ ンウィ Nwisd (ンウィスド Nwisudo) nwu んうぅ ンウゥ nwe んうぇ ンウェ Nwenaing (ンウェナイング Nwenaingu) nwo んうぉ ンウォ Nwoya District (ンウォヤ・ディストリクト Nwoya Disutorikuto) ==Stroke order== upright|alt=Stroke order in writing ん|Stroke order in writing ん upright|alt=Stroke order in writing ン|Stroke order in writing ン thumb|none|280x60px|Stroke order in writing ん thumb|none|280x60px|Stroke order in writing ン ==Other communicative representations== * Full Braille representation ん / ン in Japanese Braille: * Computer encodings N is the only Katakana without a circled form in Unicode. ==References== * Category:Specific kana
Cha Hak-yeon (, born June 30, 1990), better known by his stage name N (), is a South Korean singer, actor, presenter, and radio host, signed to 51k. He debuted as a member of the South Korean boy band VIXX in May 2012, he began his acting career in 2014 in MBC's romantic-melodrama Hotel King as Noah. He has since had roles in The Family is Coming (2015), Cheer Up! (2015), and Tomorrow Boy (2016). N began his career as a radio host in May 2015 with his show VIXX N K-pop on SBS Power FM. ==Early life== Born in Changwon, South Korea, N's family consists of himself, his parents, one older brother and two older sisters. N studied at Howon University and spent a year in Japan. Before debuting with VIXX, N participated in a musical called Gwanghwamun Love Song and entered in dance competitions. He had an extensive dance background, specializing in hip-hop, ballet, jazz and contemporary. In 2009, he participated and won various competitions held by big entertainment agencies such as SM, YG, and JYP. His blindfold dance, which he personally choreographed, won the Grand Prize at the Korean Youth Dance Festival. ==Career== ===2012–2013: Debut with VIXX and variety show appearances=== N was one of ten trainees who were contestants in Mnet's survival reality show MyDOL and was chosen to be a part of the final line-up and the 6-member boy group VIXX finally debuted with "Super Hero" on May 24, 2012 on M! Countdown. Prior to participating in MyDOL, N was featured in Brian Joo's "Let This Die" and Seo In-guk's "Shake It Up" music videos. In the year 2012, after VIXX's debut, N became a cast member in the second season of TVN's reality television show The Romantic & Idol. In 2013 with the release of VIXX's album, Jekyll N created the choreography to go along with title song "G.R.8.U" of the repackaged Hyde mini-album; he also appeared in Episode 4 of SBS's Television Drama The Heirs alongside his group members. That same year, he choreographed other VIXX performances for their song "Light Up the Darkness" and for a special performance on the show Dancing 9 with Justin Timberlake's "LoveStoned". ===2014–2015: Big Byung, acting debut, MC-ing and Radio Hosting=== In 2014, N appeared in many variety shows as a cast member such as Mnet's 4 Things Show, TVN's First Day of Work Season 3 and MBC Every 1's Hitmaker. In Hitmaker, he became a member of Jeong Hyeong-don and Defconn's first project group, Big Byung, alongside VIXX member Hyuk, Got7's Jackson and BtoB's Sungjae. Going by the stage name Dol Baeki, N and the group created two singles "Stress Come On" and "Ojingeo Doenjang" (). N was cast in his first television drama in a supporting role as Noah, a bright and lively hotel employee in MBC's romantic-melodrama Hotel King. and appeared with Hongbin as a cameo in K.Will, Mamamoo and Wheesung's "Peppermint Chocolate" music video. In 2015, N was cast in his second television drama in a supporting role as Cha Hak-yeon in SBS's The Family Is Coming and also appeared on Running Man alongside other idols, later he joined Super Junior's Eunhyuk and Kangin as cast members of MBC Every 1's Bachelor's Party. On April 25, 2015, N joined SHINee's Minho and Red Velvet's Yeri as MC on MBC's Show! Music Core from April 25, 2015 to November 14, 2015. On May 2, 2015, N's own radio show VIXX N K-pop premiered on the radio with N as the host and fellow member Ken as a fixed guest for the Quiz King segment (every Wednesday). N was also appearing on Super Junior Kiss the Radio as a fixed guest hosted by Super Junior's Ryeowook. On July 7, 2015, N went Off to School at Hyundai Chungun High School in Ulsan, South Korea for three days as a student in JTBC’s variety program Off to School alongside other celebrities. Towards the end of July, N was confirmed to join the cast in SBS's survival variety show Law of the Jungle in Nicaragua; the show aired in September. In August 2015, N was appointed as co- MC on Weekly Idol with AOA's Mina and Apink's Ha-young. He was the MC of the show with the main MC's Jeong Hyeong-don and Defconn from September 2, 2015 to March 24, 2016 In September 2015, N was cast as Ha Dong-jae, a character who is brilliant yet has an oddball personality in KBS’s drama Cheer Up! which follows the lives of students at a prestigious boarding high school as they form a cheer-leading club. ===2016–2018: Web dramas, First OST and musical theatre debut=== In February 2016, N was cast in his first web drama as Ahn Tae-pyung, a character who takes care of his grandmother and three siblings after his parents’ death in the web drama Tomorrow Boy which aired on Naver TV Cast in March. In September, N participated in his first original soundtrack for a drama. N and Melody Day’s Yeoeun released the song "Without You" () for the drama W on September 7, 2016. In the same month, N was cast alongside fellow VIXX member Lee Hong-bin and AOA’s Chanmi in the web drama What's Up With These Kids? which will air on Naver TV Cast on November 16. In November N was cast in the musical In The Heights as the lead role of Benny from December 20, 2016 to February 12, 2017 at the CJ Towol Theater in Seoul Arts Center. On July 2017, it was announced that he also co-choreographed with Jane Kim for MyTeen's debut album's Track 4 titled '꺼내가' ('Take it out). ===2019–present: Military enlistment, departure from Jellyfish, and acting=== A few months before his enlistment N created his own channel on YouTube where he would share short clips of him dancing, touring, etc. under the title "오늘의 기록" Today's Record. On March 4, 2019, N enlisted for his military service. On October 7, 2020, N was officially discharged after having completed his military service. On October 31, 2020, N left Jellyfish Entertainment after he decided not to renew his contract, he joined 51k on November 3. In 2021, N starred in the tvN drama Mine. The same year, he played a supporting role as Oh Kyung-tae, a warm-hearted police constable in tvN drama Bad and Crazy. ==Discography== ===Singles=== Title Year Peak chart position Sales Album KOR Gaon As Lead Artist "Cactus" () 2018 — rowspan="1" rowspan="1" Collaborations "Stress Come On" (with Hyuk, Jackson and Sungjae as Big Byung) 2014 — rowspan="2" rowspan="2" "Ojingeo Doenjang" () (with Hyuk, Jackson and Sungjae as Big Byung) 2015 — Original soundtracks "Without You" () (with Yeoeun of Melody Day) 2016 98 * KOR: 26,260+ W OST Part.9 "Edge" () 2018 — — Children of Nobody OST Part 4 "—" denotes releases that did not chart or were not released in that region. ===Other recordings=== Year Song Note 2015 "Higher Than Me" Shin Seung-hun cover 2017 "Tearful" Go Han-woo cover ===Songwriting credits=== Year Song Album Artist Role 2017 VIXX Lyricist and composer 2018 "Resemble" () Eau De VIXX VIXX Lyricist and composer 2019 "Walking" (걷고있다) Walking (걷고있다) VIXX Lyricist with Ravi and composer ==Filmography== ===Television series=== Year Title Role Notes 2013 The Heirs Himself Cameo with VIXX members (Episode 4) 2014 Hotel King Noah 2015 The Family is Coming Cha Hak-yeon Cheer Up! Ha Dong-jae 2017 Tunnel Park Kwang- ho Ms. Perfect Brian Lee 2018 Familiar Wife Kim Hwan Children of Nobody Lee Eun-ho 2021 Drama Stage – The Fair Go Do-young Season 4; Episode 8 Mine Han Soo-hyuk Secret Royal Inspector & Joy Choi Seung-yeol Cameo (Episode 9–10) 2021–2022 Bad and Crazy Oh Kyung-tae 2022 Tomorrow Kim Hoon Cameo (Episode 9) Drama Special – Stain Gong Ji-hoon one act-drama 2023 Joseon Attorney Yoo Ji- seon Diva of the Deserted Island Kang Woo-hak === Web shows === Year Title Role 2016 Tomorrow Boy Ahn Tae-pyung What's Up With These Kids? Choi Geum-son ===Television shows=== Year Title Role Notes 2012 The Romantic & Idol Season 2 Cast member 2014 4 Things Show Main star Hitmaker Cast member First Day Of Work Cast member Season 3 2015 Cast member Hitmaker Season 2 Show! Music Core Co-Host with Yeri (Red Velvet) and Minho (Shinee) Bachelor's Party Cast member 100 People, 100 Songs Contestant Off to School Cast member Episodes 53–56 Law of the Jungle in Nicaragua Cast member Episodes 181–184 2015–2016 Weekly Idol Assistant MC with Mina (AOA) and Oh Ha-young (Apink) 2016 Celebrity Bromance Cast member Season 7; with Lee Won-keun 2017 King of Mask Singer Contestant as "Got My Favorite Dartman" (Episode 101) Lipstick Prince Co-Host Season 2 2018 Music Bank Special MC with Ahn Sol-bin (Episode 929) 2018 Battle Trip Contestant Episode 78; with Hongbin (Episode 91-93) ===Radio shows=== Year Title Role Notes 2015 VIXX N K-pop Host from May 2, 2015 to November 2, 2015 ==Musicals== Year Title Role Notes 2011 Gwanghwamun Love Song 2016–2017 In The Heights Benny 2017–2018 Interview Gordon Sinclair 2019-2020 Return: The Promise of the Day Hae Il Military theater == Awards and nominations== Name of the award ceremony, year presented, category, nominee of the award, and the result of the nomination Award ceremony Year Category Nominee / Work Result KBS Drama Awards 2022 Best Actor in Drama Special/TV Cinema The Stains ==References== ==External links== * * Category:Jellyfish Entertainment artists Category:VIXX members Category:Japanese-language singers of South Korea Category:South Korean dance music singers Category:South Korean male idols Category:South Korean pop singers Category:South Korean male singers Category:South Korean male television actors Category:South Korean male web series actors Category:People from Changwon Category:1990 births Category:Living people Category:Howon University alumni Category:21st-century South Korean singers Category:Weekly Idol members
N 180B is an emission nebula located in the Large Magellanic Cloud. ==References== Category:Emission nebulae Category:Dorado Category:Large Magellanic Cloud
"N 2 Deep" is a song by Canadian rapper Drake featuring American rapper Future. It was released on September 3, 2021 as the eighth track from Drake's sixth studio album Certified Lover Boy. The song sampled the song Get Throwed produced by producer Leroy Williams, Jr. ==Charts== ===Weekly charts=== Chart performance for "N 2 Deep" Chart (2021) Peak position Australia Hip-Hop/R&B; Singles (ARIA) 14 France (SNEP) 58 Greece (IFPI) 46 Lithuania (AGATA) 64 Slovakia (Singles Digitál Top 100) 90 South Africa (RISA) 11 Sweden Heatseeker (Sverigetopplistan) 1 ===Year-end charts=== Year-end chart performance for "N 2 Deep" Chart (2021) Position US Hot R&B;/Hip-Hop Songs (Billboard) 97 ==References== Category:2021 songs Category:Drake (musician) songs Category:Songs written by Drake (musician) Category:Future (rapper) songs Category:Songs written by Future (rapper) Category:Songs written by Jeezy Category:Songs written by 40 (record producer) Category:Songs written by Jay-Z Category:Songs written by Pimp C
"N 2 Gether Now" is a hip hop song by the American band Limp Bizkit and the rapper Method Man. It was the third single released from their second studio album, Significant Other. The single was released with their last single "Break Stuff". The song does not include the instrumentalist members Sam Rivers and Wes Borland. ==Background== Method Man had heard about Limp Bizkit and wanted to record with them because he had never worked with a rock band. The band allowed Fred Durst and DJ Lethal to explore their hip hop origins by recording a song with the rapper. DJ Premier of Gang Starr produced the song even though he was hesitant to do so at first. According to Borland, the band wanted to record "a track that was straight hip-hop". The beginnings of the backing beat started with a demo that DJ Lethal created. Patrick Moxey, who was managing DJ Premier at the time, was contacted by Limp Bizkit, who were interested in having Premier update the existing beat. Premier had previously been aware of Limp Bizkit through their cover of "Faith" by George Michael and DJ Lethal's previous work in House of Pain, which led to him eventually agreeing to work with the band, but not without declining first. DJ Premier had hesitations around lead singer Fred Durst's rapping ability, believing it to not be at the same level as previous artists Premier had worked with. Because of this, Premier initially rejected the offer to work on the track. > "To me Fred [Durst] was dope with what they did. But when it came to the > emceeing aspect of what I was used to, I was very, very hesitant to do it. I > was like, ‘yo man, I’m just not feeling the way he raps.'" After a face-to-face meeting with Durst and learning that Method Man would be featured on the track, Premier became more interested. Durst impressed Premier by offering to work closely with him in order to improve his performance, and revealing he owned the entire DJ Premier Tape Kingz mixtape collection. Premier's biggest contributions to the track ended up being a re-recording of Durst's vocals, a complete change of the drum sounds and bass line, and the addition of samples recorded by Durst that he provided on a 10" dubplate. ==Track listing== #"Break Stuff" (album version) #"Crushed" (album version) #"N 2 Gether Now" (album version) ==References== ==External links== * Category:1999 singles Category:Limp Bizkit songs Category:Method Man songs Category:Music videos directed by Fred Durst Category:Song recordings produced by DJ Premier Category:American hip hop songs Category:Songs written by Method Man Category:Songs written by Fred Durst Category:Songs written by Wes Borland Category:Songs written by John Otto (drummer) Category:Songs written by Sam Rivers (bassist) Category:1999 songs
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics. Super Yang–Mills was studied by Julius Wess and Bruno Zumino in which they demonstrated the supergauge- invariance of the theory and wrote down its action, alongside the action of the Wess–Zumino model, another early supersymmetric field theory. The treatment in this article largely follows that of Figueroa-O'Farrill's lectures on supersymmetry and of Tong. While N = 4 supersymmetric Yang–Mills theory is also a supersymmetric Yang–Mills theory, it has very different properties to \mathcal{N} = 1 supersymmetric Yang–Mills theory, which is the theory discussed in this article. The \mathcal{N} = 2 supersymmetric Yang–Mills theory was studied by Seiberg and Witten in Seiberg–Witten theory. All three theories are based in d = 4 super Minkowski spaces. == The supersymmetric Yang–Mills action == === Preliminary treatment === A first treatment can be done without defining superspace, instead defining the theory in terms of familiar fields in non-supersymmetric quantum field theory. ==== Spacetime and matter content ==== The base spacetime is flat spacetime (Minkowski space). SYM is a gauge theory, and there is an associated gauge group G to the theory. The gauge group has associated Lie algebra \mathfrak{g}. The field content then consists of * a \mathfrak{g}-valued gauge field A_\mu * a \mathfrak{g}-valued Majorana spinor field \Psi (an adjoint- valued spinor), known as the 'gaugino' * a \mathfrak{g}-valued auxiliary scalar field D. For gauge-invariance, the gauge field A_\mu is necessarily massless. This means its superpartner \Psi is also massless if supersymmetry is to hold. Therefore \Psi can be written in terms of two Weyl spinors which are conjugate to one another: \Psi = (\lambda, \bar \lambda), and the theory can be formulated in terms of the Weyl spinor field \lambda instead of \Psi. ==== Supersymmetric pure electromagnetic theory ==== When G = U(1), the conceptual difficulties simplify somewhat, and this is in some sense the simplest gauge theory. The field content is simply a (co-)vector field A_\mu, a Majorana spinor \Phi and a auxiliary real scalar field D. The field strength tensor is defined as usual as F_{\mu u} := \partial_\mu A_ u - \partial_ u A_\mu. The Lagrangian written down by Wess and Zumino is then ::\mathcal{L} = - \frac{1}{4}F_{\mu u}F^{\mu u} - \frac{i}{2}\bar\Psi\gamma^\mu \partial_\mu\Psi + \frac{1}{2}D^2. This can be generalized to include a coupling constant e, and theta term \propto \vartheta F_{\mu u}*F^{\mu u}, where *F^{\mu u} is the dual field strength tensor :*F^{\mu u} = \frac{1}{2}\epsilon^{\mu u\rho\sigma}F_{\rho\sigma}. and \epsilon^{\mu u\rho\sigma} is the alternating tensor or totally antisymmetric tensor. If we also replace the field \Psi with the Weyl spinor \lambda, then a supersymmetric action can be written as = \int d^4x \left[-\frac{1}{4e^2}F_{\mu u}F^{\mu u} + \frac{\vartheta}{32\pi^2}F_{\mu u}*F^{\mu u} - \frac{i}{e^2}\lambda\sigma^\mu\partial_\mu \bar\lambda + \frac{1}{2e^2}D^2\right] |border |border colour =#50C878 |background colour = #ECFCF4 }} This can be viewed as a supersymmetric generalization of a pure U(1) gauge theory, also known as Maxwell theory or pure electromagnetic theory. ==== Supersymmetric Yang–Mills theory (preliminary treatment) ==== In full generality, we must define the gluon field strength tensor, : F_{\mu u} = \partial_\mu A_ u - \partial_ u A_\mu - i[A_\mu, A_ u] and the covariant derivative of the adjoint Weyl spinor, D_\mu \lambda = \partial_\mu\lambda - i[A_\mu, \lambda]. To write down the action, an invariant inner product on \mathfrak{g} is needed: the Killing form B(\cdot, \cdot) is such an inner product, and in a typical abuse of notation we write B simply as \text{Tr}, suggestive of the fact that the invariant inner product arises as the trace in some representation of \mathfrak{g}. Supersymmetric Yang–Mills then readily generalizes from supersymmetric Maxwell theory. A simple version is :S_{\text{SYM}} = \int d^4x \text{Tr}\left[-\frac{1}{4}F_{\mu u}F^{\mu u} - \frac{1}{2}\bar\Psi \gamma^\mu D_\mu \Psi\right] while a more general version is given by = \int d^4x \text{Tr}\left[-\frac{1}{2g^2}F_{\mu u}F^{\mu u} + \frac{\vartheta}{16\pi^2}F_{\mu u}*F^{\mu u} - \frac{2i}{g^2}\lambda\sigma^\mu D_\mu \bar\lambda + \frac{1}{g^2}D^2\right] |border |border colour =#50C878 |background colour = #ECFCF4 }} === Superspace treatment === ==== Superspace and superfield content ==== The base superspace is \mathcal{N} = 1 super Minkowski space. The theory is defined in terms of a single adjoint-valued real superfield V, fixed to be in Wess–Zumino gauge. ==== Supersymmetric Maxwell theory on superspace ==== The theory is defined in terms of a superfield arising from taking covariant derivatives of V: :W_\alpha = -\frac{1}{4}\mathcal{\bar D^2}\mathcal{D}_\alpha V. The supersymmetric action is then written down, with a complex coupling constant \tau = \frac{\vartheta}{2\pi} + \frac{4\pi i}{e}, as = -\int d^4x \left[\int d^2 \theta \frac{i\tau}{16\pi}W^\alpha W_\alpha + \text{h.c.}\right] |border |border colour =#50C878 |background colour = #ECFCF4 }} where h.c. indicates the Hermitian conjugate of the preceding term. ==== Supersymmetric Yang–Mills on superspace ==== For non-abelian gauge theory, instead define :W_\alpha = -\frac{1}{8}\bar\mathcal{D}^2(e^{-2V}\mathcal{D}_\alpha e^{2V}) and \tau = \frac{\vartheta}{2\pi} + \frac{4\pi i}{g}. Then the action is = -\int d^4x \text{Tr}\left[\int d^2 \theta \frac{i\tau}{8\pi}W^\alpha W_\alpha + \text{h.c.}\right] |border |border colour =#50C878 |background colour = #ECFCF4 }} == Symmetries of the action == === Supersymmetry === For the simplified Yang–Mills action on Minkowski space (not on superspace), the supersymmetry transformations are : \delta_\epsilon A_\mu = \bar\epsilon \gamma_\mu \Psi : \delta_\epsilon \Psi = -\frac{1}{2} F_{\mu u}\gamma^{\mu u}\epsilon where \gamma^{\mu u} = \frac{1}{2}(\gamma^\mu \gamma^ u - \gamma^ u \gamma^\mu). For the Yang–Mills action on superspace, since W_\alpha is chiral, then so are fields built from W_\alpha. Then integrating over half of superspace, \int d^2\theta, gives a supersymmetric action. An important observation is that the Wess–Zumino gauge is not a supersymmetric gauge, that is, it is not preserved by supersymmetry. However, it is possible to do a compensating gauge transformation to return to Wess–Zumino gauge. Then, after a supersymmetry transformation and the compensating gauge transformation, the superfields transform as :\delta A_\mu = \epsilon \sigma_\mu \bar \lambda + \lambda \sigma_\mu \bar \epsilon, :\delta \lambda = \epsilon D + (\sigma^{\mu u}\epsilon)F_{\mu u} :\delta D = i\epsilon \sigma^\mu\partial_\mu \bar \lambda - i \partial_\mu \lambda \bar \sigma^\mu \bar \epsilon. === Gauge symmetry === The preliminary theory defined on spacetime is manifestly gauge invariant as it is built from terms studied in non-supersymmetric gauge theory which are gauge invariant. The superfield formulation requires a theory of generalized gauge transformations. (Not supergauge transformations, which would be transformations in a theory with local supersymmetry). ==== Generalized abelian gauge transformations ==== Such a transformation is parametrized by a chiral superfield \Omega, under which the real superfield transforms as :V \mapsto V + i(\Omega - \Omega^\dagger). In particular, upon expanding V and \Omega appropriately into constituent superfields, then V contains a vector superfield A_\mu while \Omega contains a scalar superfield \omega, such that : A_\mu \mapsto A_\mu - 2 \partial_\mu (\text{Re}\,\omega) =: A_\mu + \partial_\mu \alpha. The chiral superfield used to define the action, : W_\alpha = -\frac{1}{4} \bar\mathcal{D}^2 \mathcal{D}_\alpha V, is gauge invariant. ==== Generalized non-abelian gauge transformations ==== The chiral superfield is adjoint valued. The transformation of V is prescribed by :e^{2V} \mapsto e^{-2i\Omega^\dagger}e^{2V}e^{2i\Omega}, from which the transformation for V can be derived using the Baker–Campbell–Hausdorff formula. The chiral superfield W_\alpha = -\frac{1}{8} \bar\mathcal{D}^2(e^{-2V} \mathcal{D}_\alpha e^{2V}) is not invariant but transforms by conjugation: :W_\alpha \mapsto e^{2i\Omega}W_\alpha e^{-2i\Omega}, so that upon tracing in the action, the action is gauge-invariant. == Extra classical symmetries == === Superconformal symmetry === As a classical theory, supersymmetric Yang–Mills theory admits a larger set of symmetries, described at the algebra level by the superconformal algebra. Just as the super Poincaré algebra is a supersymmetric extension of the Poincaré algebra, the superconformal algebra is a supersymmetric extension of the conformal algebra which also contains a spinorial generator of conformal supersymmetry S_\alpha. Conformal invariance is broken in the quantum theory by trace and conformal anomalies. While the quantum \mathcal{N} = 1 supersymmetric Yang–Mills theory does not have superconformal symmetry, quantum N = 4 supersymmetric Yang–Mills theory does. === R-symmetry === The \text{U}(1) R-symmetry for \mathcal{N} = 1 supersymmetry is a symmetry of the classical theory, but not of the quantum theory due to an anomaly. == Adding matter == === Abelian gauge === Matter can be added in the form of Wess–Zumino model type superfields \Phi. Under a gauge transformation, : \Phi \mapsto \exp(- 2iq\Omega)\Phi , and instead of using just \Phi^\dagger \Phi as the Lagrangian as in the Wess–Zumino model, for gauge invariance it must be replaced with \Phi^\dagger e^{2q V} \Phi. This gives a supersymmetric analogue to QED. The action can be written : S_{\text{SMaxwell}} + \int d^4x \, \int d^4\theta \, \Phi^\dagger e^{2qV} \Phi. For N_f flavours, we instead have N_f superfields \Phi_i, and the action can be written : S_{\text{SMaxwell}} + \int d^4x \, \int d^4\theta \, \Phi_i^\dagger e^{2q_iV} \Phi_i. with implicit summation. However, for a well- defined quantum theory, a theory such as that defined above suffers a gauge anomaly. We are obliged to add a partner \tilde \Phi to each chiral superfield \Phi (distinct from the idea of superpartners, and from conjugate superfields), which has opposite charge. This gives the action : S_{\text{SQED}} = S_{\text{SMaxwell}} + \int d^4x \, \int d^4\theta \, \Phi_i^\dagger e^{2q_iV} \Phi_i + \tilde\Phi_i^\dagger e^{-2q_iV} \tilde\Phi_i. === Non-Abelian gauge === For non-abelian gauge, matter chiral superfields \Phi are now valued in a representation R of the gauge group: \Phi \mapsto \exp(-2i\Omega)\Phi. The Wess–Zumino kinetic term must be adjusted to \Phi^\dagger e^{2V} \Phi. Then a simple SQCD action would be to take R to be the fundamental representation, and add the Wess–Zumino term: :S_{\text{SYM}} + \int d^4x \, d^4\theta \, \Phi^\dagger e^{2V} \Phi. More general and detailed forms of the super QCD action are given in that article. == Fayet–Iliopoulos term == When the center of the Lie algebra \mathfrak{g} is non-trivial, there is an extra term which can be added to the action known as the Fayet–Iliopoulos term. == References == Category:Supersymmetric quantum field theory
In mathematical physics, the 2D N = 2 superconformal algebra is an infinite- dimensional Lie superalgebra, related to supersymmetry, that occurs in string theory and two-dimensional conformal field theory. It has important applications in mirror symmetry. It was introduced by as a gauge algebra of the U(1) fermionic string. ==Definition== There are two slightly different ways to describe the N = 2 superconformal algebra, called the N = 2 Ramond algebra and the N = 2 Neveu–Schwarz algebra, which are isomorphic (see below) but differ in the choice of standard basis. The N = 2 superconformal algebra is the Lie superalgebra with basis of even elements c, Ln, Jn, for n an integer, and odd elements G, G, where r\in {\mathbb Z} (for the Ramond basis) or r\in {1\over 2}+{\mathbb Z} (for the Neveu–Schwarz basis) defined by the following relations: ::c is in the center ::[L_m,L_n] = \left(m-n\right) L_{m+n} + {c\over 12} \left(m^3-m\right) \delta_{m+n,0} ::[L_m,\,J_n]=-nJ_{m+n} ::[J_m,J_n] = {c\over 3} m\delta_{m+n,0} ::\\{G_r^+,G_s^-\\} = L_{r+s} + {1\over 2} \left(r-s\right) J_{r+s} + {c\over 6} \left(r^2-{1\over 4}\right) \delta_{r+s,0} ::\\{G_r^+,G_s^+\\} = 0 = \\{G_r^-,G_s^-\\} ::[L_m,G_r^{\pm}] = \left( {m\over 2}-r \right) G^\pm_{r+m} ::[J_m,G_r^\pm]= \pm G_{m+r}^\pm If r,s\in {\mathbb Z} in these relations, this yields the N = 2 Ramond algebra; while if r,s\in {1\over 2}+{\mathbb Z} are half-integers, it gives the N = 2 Neveu–Schwarz algebra. The operators L_n generate a Lie subalgebra isomorphic to the Virasoro algebra. Together with the operators G_r=G_r^+ + G_r^-, they generate a Lie superalgebra isomorphic to the super Virasoro algebra, giving the Ramond algebra if r,s are integers and the Neveu–Schwarz algebra otherwise. When represented as operators on a complex inner product space, c is taken to act as multiplication by a real scalar, denoted by the same letter and called the central charge, and the adjoint structure is as follows: :{L_n^*=L_{-n}, \,\, J_m^*=J_{-m}, \,\,(G_r^\pm)^*=G_{-r}^\mp, \,\,c^*=c} ==Properties== *The N = 2 Ramond and Neveu–Schwarz algebras are isomorphic by the spectral shift isomorphism \alpha of : \alpha(L_n)=L_n +{1\over 2} J_n + {c\over 24}\delta_{n,0} \alpha(J_n)=J_n +{c\over 6}\delta_{n,0} \alpha(G_r^\pm)=G_{r\pm {1\over 2}}^\pm with inverse: \alpha^{-1}(L_n)=L_n -{1\over 2} J_n + {c\over 24}\delta_{n,0} \alpha^{-1}(J_n)=J_n -{c\over 6}\delta_{n,0} \alpha^{-1}(G_r^\pm)=G_{r\mp {1\over 2}}^\pm *In the N = 2 Ramond algebra, the zero mode operators L_0, J_0, G_0^\pm and the constants form a five-dimensional Lie superalgebra. They satisfy the same relations as the fundamental operators in Kähler geometry, with L_0 corresponding to the Laplacian, J_0 the degree operator, and G_0^\pm the \partial and \overline{\partial} operators. *Even integer powers of the spectral shift give automorphisms of the N = 2 superconformal algebras, called spectral shift automorphisms. Another automorphism \beta, of period two, is given by \beta(L_m) = L_m , \beta(J_m)=-J_m-{c\over 3} \delta_{m,0}, \beta(G_r^\pm)=G_r^\mp In terms of Kähler operators, \beta corresponds to conjugating the complex structure. Since \beta\alpha \beta^{-1}=\alpha^{-1}, the automorphisms \alpha^2 and \beta generate a group of automorphisms of the N = 2 superconformal algebra isomorphic to the infinite dihedral group {\Z}\rtimes {\Z}_2. *Twisted operators {\mathcal L}_n=L_n+ {1\over 2} (n+1)J_n were introduced by and satisfy: [{\mathcal L}_m,{\mathcal L}_n] = (m-n) {\mathcal L}_{m+n} so that these operators satisfy the Virasoro relation with central charge 0. The constant c still appears in the relations for J_m and the modified relations [{\mathcal L}_m,J_n] = -nJ_{m+n} + {c \over 6} \left(m^2 + m \right) \delta_{m+n,0} \\{G_r^+,G_s^-\\} = 2{\mathcal L}_{r+s}-2sJ_{r+s} + {c\over 3} \left(m^2+m\right) \delta_{m+n,0} ==Constructions== ===Free field construction=== give a construction using two commuting real bosonic fields (a_n), (b_n) : {[a_m,a_n]={m\over 2}\delta_{m+n,0},\,\,\,\, [b_m,b_n]={m\over 2}\delta_{m+n,0}}, \,\,\,\, a_n^*=a_{-n},\,\,\,\, b_n^*=b_{-n} and a complex fermionic field (e_r) : \\{e_r,e^*_s\\}=\delta_{r,s},\,\,\,\, \\{e_r,e_s\\}=0. L_n is defined to the sum of the Virasoro operators naturally associated with each of the three systems :L_n = \sum_m : a_{-m+n} a_m : + \sum_m : b_{-m+n} b_m : + \sum_r \left(r+{n\over 2}\right): e^*_{r}e_{n+r} : where normal ordering has been used for bosons and fermions. The current operator J_n is defined by the standard construction from fermions :J_n = \sum_r : e_r^*e_{n+r} : and the two supersymmetric operators G_r^\pm by : G^+_r=\sum (a_{-m} + i b_{-m}) \cdot e_{r+m},\,\,\,\, G_r^-=\sum (a_{r+m} - ib_{r+m}) \cdot e^*_{m} This yields an N = 2 Neveu–Schwarz algebra with c = 3\. ===SU(2) supersymmetric coset construction=== gave a coset construction of the N = 2 superconformal algebras, generalizing the coset constructions of for the discrete series representations of the Virasoro and super Virasoro algebra. Given a representation of the affine Kac–Moody algebra of SU(2) at level \ell with basis E_n,F_n,H_n satisfying :[H_m,H_n]=2m\ell\delta_{n+m,0}, :[E_m,F_n]=H_{m+n}+m \ell\delta_{m+n,0}, :[H_m,E_n]=2E_{m+n}, :[H_m,F_n]=-2F_{m+n}, the supersymmetric generators are defined by : G^+_r = (\ell/2+ 1)^{-1/2} \sum E_{-m} \cdot e_{m+r}, \,\,\, G^-_r = (\ell/2 +1 )^{-1/2} \sum F_{r+m}\cdot e_m^*. This yields the N=2 superconformal algebra with :c=3\ell/(\ell+2) . The algebra commutes with the bosonic operators :X_n=H_n - 2 \sum_r : e_r^*e_{n+r} :. The space of physical states consists of eigenvectors of X_0 simultaneously annihilated by the X_n's for positive n and the supercharge operator :Q=G_{1/2}^+ + G_{-1/2}^- (Neveu–Schwarz) :Q=G_0^+ +G_0^-. (Ramond) The supercharge operator commutes with the action of the affine Weyl group and the physical states lie in a single orbit of this group, a fact which implies the Weyl-Kac character formula. ===Kazama–Suzuki supersymmetric coset construction=== generalized the SU(2) coset construction to any pair consisting of a simple compact Lie group G and a closed subgroup H of maximal rank, i.e. containing a maximal torus T of G, with the additional condition that the dimension of the centre of H is non-zero. In this case the compact Hermitian symmetric space G/H is a Kähler manifold, for example when H=T. The physical states lie in a single orbit of the affine Weyl group, which again implies the Weyl–Kac character formula for the affine Kac–Moody algebra of G. ==See also== *Virasoro algebra *Super Virasoro algebra *Coset construction *Type IIB string theory ==Notes== ==References== * * * * * * * * * * * * Category:String theory Category:Conformal field theory Category:Lie algebras Category:Representation theory Category:Supersymmetry
In string theory, N = 2 superstring is a theory in which the worldsheet admits N = 2 supersymmetry rather than N = 1 supersymmetry as in the usual superstring. The target space (a term used for a generalization of space-time) is four-dimensional, but either none or two of its dimensions are time-like, i.e. it has either 4+0 or 2+2 dimensions. The spectrum consists of only one massless scalar, which describes gravitational fluctuations of self-dual gravity. The target space theory is therefore self-dual gravity, and is thought to consist no local (or propagating) degrees of freedom. ==References== Category:String theory
N = 4 supersymmetric Yang–Mills (SYM) theory is a relativistic conformally invariant Lagrangian gauge theory describing fermions interacting via gauge field exchanges. In D=4 spacetime dimensions, N=4 is the maximal number of supersymmetries or supersymmetry charges. It is a toy theory based on Yang–Mills theory that does not model the real world, but is useful because it can act as a proving ground for approaches for attacking problems in more complex theories. It describes a universe containing boson fields and fermion fields which are related by four supersymmetries (this means that transforming bosonic and fermionic fields in a certain way leaves the theory invariant). It is one of the simplest (in the sense that it has no free parameters except for the gauge group) and one of the few finite quantum field theories in 4 dimensions. It can be thought of as the most symmetric field theory that does not involve gravity. Like all supersymmetric field theories, it may equivalently be formulated as a superfield theory on an extended superspace in which the spacetime variables are augmented by a number of anticommuting Grassmann variables which, for the case N=4, consist of 4 Dirac spinors, making a total of 16 independent anticommuting generators for the extended ring of superfunctions. The field equations are equivalent to the geometric condition that the supercurvature 2-form vanish identically on all super null lines. This is also known as the super-ambitwistor correspondence. A similar super-ambitwistor characterization holds for D=10, N=1 dimensional super Yang- Mills theory, and the lower dimensional cases D=6, N=2 and D=4, N=4 may be derived from this via dimensional reduction. ==Meaning of N and numbers of fields == In N supersymmetric Yang–Mills theory, N denotes the number of independent supersymmetric operations that transform the spin-1 gauge field into spin-1/2 fermionic fields."N = 4: Maximal Particles for Maximal Fun", from 4 gravitons blog (2013) In an analogy with symmetries under rotations, N would be the number of independent rotations, N = 1 in a plane, N = 2 in 3D space, etc... That is, in a N = 4 SYM theory, the gauge boson can be "rotated" into N = 4 different supersymmetric fermion partners. In turns, each fermion can be rotated into four different bosons: one corresponds to the rotation back to the spin-1 gauge field, and the three others are spin-0 boson fields. Because in 3D space one may use different rotations to reach a same point (or here the same spin-0 boson), each spin-0 boson is superpartners of two different spin-1/2 fermions, not just one. So in total, one has only 6 spin-0 bosons, not 16. Therefore, N = 4 SYM has 1 + 4 + 6 = 11 fields, namely: one vector field (the spin-1 gauge boson), four spinor fields (the spin-1/2 fermions) and six scalar fields (the spin-0 bosons). N = 4 is the maximum number of independent supersymmetries: starting from a spin-1 field and using more supersymmetries, e.g., N = 5, only rotates between the 11 fields. To have N > 4 independent supersymmetries, one needs to start from a gauge field of spin higher than 1, e.g., a spin-2 tensor field such as that of the graviton. This is the N = 8 supergravity theory. In quantum chromodynamics (QCD), the gauge symmetry transforms a quark of a given color into a quark of another color. Therefore, in the context of QCD, N corresponds to the number of colors and N = 4 SYM is a toy model in which there are four colors (in Nature, QCD has N = 3 colors). ==Lagrangian== The Lagrangian for the theory is : L = \operatorname{tr} \left\\{-\frac{1}{2g^2}F_{\mu u}F^{\mu u}+\frac{\theta_I}{8\pi^2}F_{\mu u}\bar{F}^{\mu u}- i \overline{\lambda}^a\overline{\sigma}^\mu D_\mu \lambda_a -D_\mu X^i D^\mu X^i +g C^{ab}_i \lambda_a[X^i,\lambda_b] + g \overline{C}_{iab}\overline{\lambda}^a[X^i,\overline{\lambda}^b]+\frac{g^2}{2}[X^i,X^j]^2 \right\\}, where g and \theta_I are coupling constants (specifically g is the gauge coupling and \theta_I is the instanton angle), the field strength is F^k_{\mu u} = \partial_\mu A^k_ u-\partial_ u A^k_\mu+f^{klm}A^l_\mu A^m_ u with A^k_ u the gauge field and indices i,j = 1, ..., 6 as well as a, b = 1, ..., 4, and f represents the structure constants of the particular gauge group. The \lambda^a are left Weyl fermions, \sigma^\mu are the Pauli matrices, D_\mu is the gauge covariant derivative, X^i are real scalars, and C_i^{ab} represents the structure constants of the R-symmetry group SU(4), which rotates the four supersymmetries. As a consequence of the nonrenormalization theorems, this supersymmetric field theory is in fact a superconformal field theory. ==Ten- dimensional Lagrangian== The above Lagrangian can be found by beginning with the simpler ten-dimensional Lagrangian : L = \operatorname{tr} \left\\{ \frac{1}{g^2} F_{IJ} F^{IJ} - i \bar{\lambda} \Gamma^I D_I \lambda \right\\}, where I and J are now run from 0 through 9 and \Gamma^I are the 32 by 32 gamma matrices ( 32=2^{10/2} ), followed by adding the term with \theta_I which is a topological term. The components A_i of the gauge field for i = 4 to 9 become scalars upon eliminating the extra dimensions. This also gives an interpretation of the SO(6) R-symmetry as rotations in the extra compact dimensions. By compactification on a T6, all the supercharges are preserved, giving N = 4 in the 4-dimensional theory. A Type IIB string theory interpretation of the theory is the worldvolume theory of a stack of D3-branes. ==S-duality== The coupling constants \theta_I and g naturally pair together in the form: : \tau = \frac{\theta}{2\pi}+\frac{4\pi i}{g^2}. The theory has symmetries that shift \tau by integers. The S-duality conjecture says there is also a symmetry which sends : \tau \mapsto \frac{-1}{n_G\tau} as well as switching the group G to its Langlands dual group. ==AdS/CFT correspondence== This theory is also important in the context of the holographic principle. There is a duality between Type IIB string theory on AdS5 × S5 space (a product of 5-dimensional AdS space with a 5-dimensional sphere) and N = 4 super Yang–Mills on the 4-dimensional boundary of AdS5. However, this particular realization of the AdS/CFT correspondence is not a realistic model of gravity, since gravity in our universe is 4-dimensional. Despite this, the AdS/CFT correspondence is the most successful realization of the holographic principle, a speculative idea about quantum gravity originally proposed by Gerard 't Hooft, who was expanding on work on black hole thermodynamics, and was improved and promoted in the context of string theory by Leonard Susskind. ==Integrability == There is evidence that N = 4 supersymmetric Yang–Mills theory has an integrable structure in the planar large N limit (see below for what "planar" means in the present context). As the number of colors (also denoted N) goes to infinity, the amplitudes scale like N^{2-2g}, so that only the genus 0 (planar graph) contribution survives. Planar Feynman diagrams are graphs in which no propagator cross over another one, in contrast to non-planar Feynman graphs where one or more propagator goes over another one."Planar vs. Non-Planar: A Colorful Story", from 4 gravitons blog (2013) A non-planar graph has a smaller number of possible gauge loops compared to a similar planar graph. Non-planar graphs are thus suppressed by factors 1/N^{2-2g} compared to planar ones which therefore dominate in the large N limit. Consequently, a planar Yang–Mills theory denotes a theory in the large N limit, with N usually the number of colors. Likewise, a planar limit is a limit in which scattering amplitudes are dominated by Feynman diagrams which can be given the structure of planar graphs.planar limit in nLab In the large N limit, the coupling g vanishes and a perturbative formalism is therefore well-suited for large N calculations. Therefore, planar graphs are associated to the domain where perturbative calculations converge well. Beisert et al. give a review article demonstrating how in this situation local operators can be expressed via certain states in spin chains (in particular the Heisenberg spin chain), but based on a larger Lie superalgebras rather than \mathfrak{su}(2) for ordinary spin. These spin chains are integrable in the sense they can be solved by the Bethe ansatz method. They also construct an action of the associated Yangian on scattering amplitudes. Nima Arkani-Hamed et al. have also researched this subject. Using twistor theory, they find a description (the amplituhedron formalism) in terms of the positive Grassmannian. ==Relation to 11-dimensional M-theory== N = 4 super Yang–Mills can be derived from a simpler 10-dimensional theory, and yet supergravity and M-theory exist in 11 dimensions. The connection is that if the gauge group U(N) of SYM becomes infinite as N\rightarrow \infty it becomes equivalent to an 11-dimensional theory known as matrix theory. == See also == * 6D (2,0) superconformal field theory * Extended supersymmetry * N = 1 supersymmetric Yang–Mills theory * N = 8 supergravity * Seiberg–Witten theory == References == === Citations === === Sources === * Category:Supersymmetric quantum field theory Category:Conformal field theory
In four spacetime dimensions, N = 8 supergravity is the most symmetric quantum field theory which involves gravity and a finite number of fields. It can be found from a dimensional reduction of 11D supergravity by making the size of seven of the dimensions go to zero. It has eight supersymmetries, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin −2. (The spin 2 graviton is the particle with the highest spin in this theory.) More supersymmetries would mean the particles would have superpartners with spins higher than 2. The only theories with spins higher than 2 which are consistent involve an infinite number of particles (such as String Theory and Higher-Spin Theories). Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything. However, in later years this was abandoned in favour of string theory. There has been renewed interest in the 21st century, with the possibility that this theory may be finite. ==Calculations== It has been found recently that the expansion of N = 8 supergravity in terms of Feynman diagrams has shown that N = 8 supergravity is in some ways a product of two N = 4 super Yang–Mills theories. This is written schematically as: : N = 8 supergravity = (N = 4 super Yang–Mills) × (N = 4 super Yang–Mills) This is not surprising, as N = 8 supergravity contains six independent representations of N = 4 super Yang–Mills. ==Particle content== The theory contains 1 graviton (spin 2), 8 gravitinos (spin 3/2), 28 vector bosons (spin 1), 56 fermions (spin 1/2), 70 scalar fields (spin 0) where we don't distinguish particles with negative spin. These numbers are simple combinatorial numbers that come from Pascal's Triangle and also the number of ways of writing n as a sum of 8 nonnegative cubes A173681. One reason why the theory was abandoned was that the 28 vector bosons which form an O(8) gauge group is too small to contain the standard model U(1) x SU(2) x SU(3) gauge group, which can only fit within the orthogonal group O(10). For model building, it has been assumed that almost all the supersymmetries would be broken in nature, leaving just one supersymmetry (N = 1), although nowadays because of the lack of evidence for N = 1 supersymmetry higher supersymmetries are now being considered such as N = 2\. ==Connection with superstring theory== N = 8 supergravity can be viewed as the low-energy approximation of the type IIA or type IIB superstring with 6 of its dimensions compactified on a 6-torus. Equivalently, it may also be viewed as 11D M-theory with seven of its dimensions compactified on a 7-torus. ==Global symmetries== Some surprising global symmetries have been found in this theory. For example, it has been shown that there is an E7 global symmetry but in order for the theory to be finite it is thought that there may be other symmetries not yet found. ==See also== * Pure 4D N = 1 supergravity ==References== Category:Supersymmetric quantum field theory Category:Theories of gravity
Justice N Anand Venkatesh is a sitting Judge of the Charted High Court of Madras. == Early life == N Anand Venkatesh was born on 4 July 1969. He studied in St. Mary’s School at Perambur. He graduated with Bachelor of Commerce from A.M. Jain College, Meenambakkam and Bachelor of Law from Ambedkar Law college, Chennai. == Judge of High Court == The Collegium headed by Chief Justice of the Madras High Court S K Kaul recommended the appointment of N Anand Venkatesh as an Additional Judge of Madras High Court on 19 December 2016. The recommendation was cleared by the Supreme Court collegium in December 2017 and he was appointed on 4 June 2018. The Collegium headed by Chief Justice of India S A Bobde in a meeting held on 12 February 2020 approved the appointment of N Anand Venkatesh as Permanent Judge of Madras High Court. == Notable judgments == === LGBTQ Rights === ==== S Sushma v. Commissioner of Police ==== On 28 April 2021, Madras High Court Justice N Anand Venkatesh passed an interim order in response to a petition filed by two young women with same sex orientation. According to the order, in an unprecedented move, he decided to undergo psycho-education before penning a judgment on same sex relationships.Judge said that psyhco-educative counseling on queer issues helped him shed his personal ignorance and prejudices. He clearly stated in the judgment that the responsibility to change, the burden of unlearning stigma, and learning about the lived experience of the queer community lies on the society and not the queer individuals. The court recognized that there’s an absence of a specific law to protect the interests of queer people and acknowledged it is the responsibility of the constitutional courts to fill this vacuum with necessary directions to ensure the protection of such couples from harassment sourced from stigma and prejudices. On 7 June 2021, in delivering the verdict on this case, Justice N Anand Venkatesh prohibited Conversion Therapy. He suggested comprehensive measures to sensitize the society and various branches of the State including the Police and judiciary to remove prejudices against the LGBTQIA+ community. He suggested that changes be made to the curricula of schools and universities to educate students on understanding the LGBTQIA+ community. > "This Court is unable to understand the need for such a knee-jerk reaction > within hours of the material getting uploaded on the website. If someone > really had a grievance, the same should have been addressed in a proper > manner through proper consultation and meetings, and no one can be allowed > to arm-twist a State-run council into forcibly withdrawing a material that > came out after a long study by a committee." — Justice N Anand Venkatesh, > about the withdrawal of the NCERT report on gender non-conforming and > transgender children from its official website. The report titled 'Inclusion of Transgender Children in School Education: Concerns and Roadmap' was taken down within hours of its publishing, owing to external pressure. The report, which was meant as training material for educators at schools, was removed from the site after the NCPCR (National Commission for Protection of Child Rights) sent a notice to the NCERT against the manual following complaints raised against the material from certain sections. Justice N Anand Venkatesh, on addressing the needs of transgender children and those with binary identities, noted that sensitization has to start from schools and home, and without family support, children belonging to the community would never be able to get support elsewhere. The court reasoned that the report of an expert body cannot be disregarded due to opposition from a few quarters that still hesitate to recognize the LGBTQIA+ Community. The judge directed the NCERT to submit its report on the issue before the court on 23 December. == References == == External links == * Category:Judges of the Madras High Court Category:Judges of the High Courts of India Category:Indian judges Category:1969 births Category:Living people
N Parachute Battery (The Eagle Troop) Royal Horse Artillery is a Tactical Group Battery of 7th Parachute Regiment Royal Horse Artillery. They are currently based in Albemarle Barracks in Northumberland. The battery is commonly known as a Tactical Group Battery and provides the artillery support to the Royal Irish Battle Group 16 Air Assault Brigade Combat Team. ==Current role== N Parachute Battery (The Eagle Troop) are currently serving as the Tactical Group within 7 Para RHA and supports 16 Air Assault Brigade Combat Team. ===Battery structure=== N Parachute Battery are known as a Tactical Group Battery and they consist of approximately 30 personnel: * Battery Commanders Tac Group * FST Party 1 * FST Party 2 * FST Party 3 * Joint Fires Cell (JFC) * Tactical Air Control Party (TACP) ==History== ===Formation=== 1st Troop Bombay Horse Artillery was formed in Seroor, on 11 November 1811. ===19th century=== In 1842 Sir Charles Napier was sent to Hyderabad with a treaty that was never to be accepted by the Amirs of Sindh. The Amirs attacked the British Residency, and Napier decided this was cause for war, and attacked a force of 22,000 Baluchis with just 2,800 British Soldiers. This resulted in: * 1843 – The Battle for Miani. The British line held, and 6 guns from the Troop supported a charge. Hyderabad was occupied in February 1843. The battery was awarded its honour title following Sir Charles Napier's march to the Indus River. The troop were supporting the Cheshire Regiment, with the enemy in an entrenched position. The way artillery was deployed, forced the enemy to its left flank, which allowed the Cheshire Regiment to advance and distract the enemy. A surrender followed quickly and the Governor-General of India, the Lord Ellenborough, declared that the battery should, 'bear the eagle'. In 1858, the East India Company dissolved, and the battery became part of the British Army. The battery was renamed five times between 1862, until it was finally named N Battery Royal Horse Artillery in 1889. ===World War One=== * 1914 – The battery deployed to France on the outbreak of War. * 1915 – The battery fired its guns in the Battle of Neuve Chapelle. The failure of this battle was later credited to the lack of artillery shells in Shell Crisis of 1915. * 1916 – The battery fought in the Battle of the Somme * 1917 – N Battery RHA claimed the highest number of shells fired in one month by a single battery. The six guns fired 115,360 rounds in August 1917 in support of the Canadian Corps. The battery also fought in the Battle of Cambrai (1917) and at Hailles. * 1918 – The battery continued to fight until the Armistice in November 1918. * 1920 – The battery bore the coffin of the Unknown Soldier to Westminster Abbey. ===World War Two=== * 1938 – The battery was merged with L (Nery) Battery and was known as L/N (Nery) Battery within 2nd Regiment, Royal Horse Artillery. * 1939 – The battery formed part of the British Expeditionary Force, and fought in France until the Dunkirk evacuation in 1940 The battery served in Greece and the Western Desert, and in 1942 regained its identity and joined 6th Regiment, Royal Horse Artillery. ===Cold War=== In 1951, The battery was part of 4 RHA within 7 Armoured Division based at Hohne Germany until 1958 * 1958 – The battery deployed to Malaya during the Malayan Emergency * 1961 – The battery moved to Colchester, as part of the Strategic Reserve. During this time it was deployed to Cyprus to prevent further fighting between Greek and Turkish Cypriots * 1965 – The battery moved to Münster. ==Recent and Current Conflicts== ===Northern Ireland=== * 1968 – The battery moved to Barnard Castle in Yorkshire. * 1971 – The battery moved to Deilinghofen in West Germany. During this time the battery completed three tours of Northern Ireland, including a posting to Andersonstown, West Belfast in 1972, HM Prison Maze, Lisburn in September 1973 and the Bogside in Derry in 1975. * 1977 – The battery moved to Dortmund, immediately followed by a further posting to Craigavon, Northern Ireland in 1977. * 1980 – The battery moved to Larkhill * 1982 – The battery returned to Münster. * 1993 – 2nd Field Regiment RA disbanded and N Battery joined 3rd Regiment Royal Horse Artillery in Topcliffe, Yorkshire. ===Balkan wars=== The battery served in the Balkans. ===Operation TELIC in Iraq=== *2004 – L / N Battery served in Iraq on Op TELIC 4, as part of 1st Regiment, Royal Horse Artillery. ===Operation HERRICK in Afghanistan === * 2006 - OP HERRICK 8 * 2010 – OP HERRICK 13 * 2013 – OP HERRICK 19 === Re-Subordination to 7th Parachute Regiment Royal Horse Artillery === * 2023 – 22 May 23 N Parachute Battery forms as sub-unit to 7 Para RHA. The Battery support the Royal Irish Regiment within 16 Air Assault Brigade Combat Team. ==See also== *British Army *Royal Artillery *Royal Horse Artillery *List of Royal Artillery Batteries *Bombay Horse Artillery Batteries == References == ==Bibliography== * ==External links== * * * Category:Royal Horse Artillery batteries Category:Royal Artillery batteries Category:1811 establishments in British India Category:Military units and formations established in 1811
N Brown Group plc () is an online retailer headquartered in Manchester, England. N Brown offers a range of products, predominantly clothing, footwear and homewares with a focus on underserved customer groups. The company is listed on the London Stock Exchange. ==History== The oldest company within the group - JD Williams & Company Ltd - was founded by James David Williams in 1859 when he started in business operating three mobile shops. In 1882, he took advantage of the introduction of UK's parcel post service, to send his company's products direct to his customers. In 1907, JD Williams instructed architect R Argile to build Langley Buildings in a baroque style on Dale Street in Manchester's Northern Quarter: this building still stands today. In 1963, All Williams' family shares were bought by Cooper-Taymil Ltd (a subsidiary of Alliance Brothers Ltd. owned by Lord (David) Alliance CBE and Sir Nigel Alliance OBE) and placed in a holding company, N Brown Investments, (founded by Nathan Brown in 1964 and acquired by David Alliance in 1968). In 1970, N Brown Group acquired JD Williams shares along with mail-order catalogues Ambrose Wilson and Oxendales. In 1986, N Brown Investments acquired the JD Williams group in a reverse takeover to secure a public quotation. The company name was changed to N Brown Group plc. In 2004, the business moved to new premises on Lever Street in Manchester's Northern Quarter. The company bought online underwear retailer Figleaves for £11.5 million in 2010. Lord Alliance stepped down as chairman in 2012 with Andrew Higginson joining that September. In 2014, N Brown outsourced 550 contact centre roles to Serco. That year it also issued two profit warnings within six months. Angela Spindler joined as Chief Executive in 2013, succeeding Alan White, who had been in the top job since 1984. In 2017, shares fell by as much as 9pc when N Brown announced it was facing a £40m hit after finding issues with a credit insurance product it sold to customers between 2006 and 2014, responding to a crackdown by the Financial Conduct Authority. In 2018, Matt Davies was announced as the new chairman of N Brown Group. In 2020, N Brown took a range of actions to retain cash after sales fell by 40%. It established a £50 million three-year lending facility under the Coronavirus Large Business Interruption Loan Scheme supported by borrowers. It also broadened curtained covenants in its existing £125 million unsecured revolving credit facility in anticipation of the half-year test date of August 2020. Following the COVID-19 pandemic and subsequent lock down, the company suffered a sharp decline in revenue in March 2020 and then, in August 2020, suspended its dividend for the financial year ending in February 2021. == Brands == In 1999, Simply Be was launched to cater for women aged 25 – 45 in sizes 12 - 32 and has been a vocal champion of size inclusivity. In 2007, Jacamo was launched, catering for 25 - 45-year-old men of all body shapes, from small to 5XL. Former cricketer Freddie Flintoff was recently a key brand ambassador. In 2018, JD Williams rebranded to become JD Williams: The Life Store, positioning the brand as a modern online department store for the 45 – 60-year-old woman. Home Essentials, Fashion World, Marisota, Ambrose Wilson and Premier Man are also operated by N Brown as well as the Ireland-based Oxendales. == Stores == Simply Be, Jacamo and High & Mighty operated bricks & mortar stores throughout the UK until 2018. The company announced it was closing five loss-making stores in 2017 and, after announcing, in June 2018, that it was proposing to close all bricks and mortar stores, the company had completely implemented that decision by August 2018. == Charity == In September 2017, N Brown donated £50,000 to the Royal Manchester Children's Hospital following the Manchester Arena bombing. ==Locations== The business has its operational Head Office in Manchester's Northern Quarter and has warehousing and distribution centres in Oldham, in Greater Manchester, and Glossop in Derbyshire. ==References== ==External links== * Category:1859 establishments in England Category:British companies established in 1859 Category:Companies based in Manchester Category:Companies listed on the London Stock Exchange Category:Online retailers of the United Kingdom Category:Retail companies established in 1859
N Carinae is a single star in the constellation Carina, just to the northeast of the prominent star Canopus. This object has a white hue and is faintly visible to the naked eye with an apparent visual magnitude of 4.35. Based on parallax, it is located at a distance of approximately 1,360 light years from the Sun. It has an absolute magnitude of −3.75, and is drifting further away with a radial velocity of +22.5 km/s. This object has a stellar classification of A0II, matching a massive bright giant. In the past it had received a class of B9III, which is sometimes still used. The star is 37 million years old with 7.9 times the mass of the Sun. It is spinning with a projected rotational velocity of 47 km/s. N Carinae is radiating 3,411 times the luminosity of the Sun from its photosphere at an effective temperature of 8,004 K. == References == Category:A-type bright giants Carinae, N Category:Carina (constellation) Category:Durchmusterung objects 047306 031407 2435
N Centauri is a binary star in the southern constellation of Centaurus. The brighter star is dimly visible to the naked eye with an apparent visual magnitude of 5.26, and it is approximately 304 light years away based on parallax. It has an absolute magnitude of +0.76 and is drifting further away from the Sun with a radial velocity of +27 km/s. It is a candidate member of the Sco OB2 moving group. The double nature of this system was discovered by German astronomer Carl Rümker in 1835. As of 2016, the companion lay at an angular separation of along a position angle of 289° from the primary. They form a co-moving pair with a projected separation of . The more luminous member is a B-type main-sequence star with a stellar classification of B9V. Its fainter companion is an F-type main-sequence star with a class of F0Vn, where the 'n' suffix indicates that the metal absorption lines in its spectrum are unusual broad ("nebulous") and indicative of rapid rotation. Based upon discrepancies in the proper motion measurements, there are hints of a third member of this system. == References == Category:B-type main-sequence stars Category:F-type main-sequence stars Category:Double stars Centauri, N Category:Durchmusterung objects Category:Centaurus 120642 067703 5207
The N-Choe is a seasonal stream (the word "choe" means stream in Punjabi) that originates in Chandigarh, India and runs across the Leisure Valley to Kajheri, Mohali (now known as Sahibzada Ajit Singh Nagar) Punjab, India, and later merges into the Ghaggar River.N-choe: Stream of filth: The Tribune 5 April 2010 The stream runs across Leisure Valley and the PCA Cricket Stadium. It is one of the seasonal rivulets in Chandigarh, which include Sukhna Choe in the East and Patiala Ki Rao in the West. The Choe Nala originates at sector 29 in Chandigarh, Punjab.chandigarh.gov.in: Geology of Chandigarh It is known as Naalaa, Stadium Wala Naalaa or Ataawa choe among locals. ==Route== ===Chandigarh=== The N-choe originates near Punjab Civil Secretariat in sector 2, Chandigarh and passes through Bougainvillea Park in sector 3, Leisure valley park in sector 10, Rose Garden and Shanti Kunj Garden in sector 16 and then through sectors 23, 36, 42, 53, next to village Kajheri in sector 52, next to Burail Jail in sector 51 in Chandigarh. ===Mohali=== From sector 51 in Chandigarh, N Choe enters Mohali and goes through the sectors 62, 63 Phase 9, 67, 81 and to the Chilla Manauli village. The stream then flows towards Patiala district and enters the Ghaggar river in Haryana.N-Choe continues to raise a stink in sector 67: Hindustan Times, 6 Oct 2012 ==Pollution == On 31 July 2010, Punjab Pollution Control Board reported that effluents discharged in N-Choe from Chandigarh were beyond the permissible limit. The analysis revealed that pollution levels such as BOD-150 mg/1 and COD 320 mg/1 was found to be more than the permissible limit of 30 mg/1 and 250 mg/1, respectively.'Effluent discharge in N-Choe beyond permissible limit': Times of India, 31 July 2010 Mohali residents complained that the N-choe was not properly protected and that sewage was found in the water.Untreated sewage being discharged in N-choe, admits GMADA in RTI reply: Indian Express, 05/2010 ==References== Category:Mohali Category:Landforms of Chandigarh Category:Rivers of Himachal Pradesh
N Dis Life is the fourth and final album of original music by Hawaiian singer Israel "Iz" Kamakawiwo'ole before his death, released in 1996. It reached #3 at Top World Music Albums. == Track listing == #"Hiʻilawe" (traditional) – 4:44 #"In This Life" (Reid, Shamblin) – 4:09 #"Waiʻalae" (traditional) – 2:43 #"Starting All Over Again" (Mitchell) – 3:59 #"Living in a Sovereign Land" (Cambern, Kamakawiwoʻole) – 4:38 #"ʻOpae E" (Aluki, Paki) – 4:09 #"Aloha Kuʻu Pua" (Isaacs) – 2:30 #"Johnny Mahoe" (Beazley) – 4:54 #"Lover of Mine" (Bilyeu, Holomalia) – 2:45 #"Yokozuna" (Chock) – 3:39 #"Na Ka Pueo/Keyhole Hula" (Machado, traditional) – 4:40 #"The Fly" (traditional) – 2:27 == References == Category:1996 albums Category:Israel Kamakawiwoʻole albums Category:Na Hoku Hanohano Award-winning albums
The N E Manion Cup is an Australian Turf Club Group 3 Thoroughbred quality handicap horse race for three year olds and upwards over a distance of 2400 metres, held annually at Rosehill Racecourse in Sydney, Australia in March. Total prizemoney for the race is A$200,000. ==History== The race is named in honour of N. E. Manion, former director of the Sydney Turf Club. ===Grade=== * 1973-1978 - Principal Race * 1979-2005 - Group 3 * 2006-2013 - Listed Race * 2014 onwards - Group 3 ===Distance=== * 1973-1978 - 2000 metres * 1979 onwards - 2400 metres ==Winners== * 2023 - Timour * 2022 - No Compromise * 2021 - Favorite Moon * 2020 - Young Rascal * 2019 - Midterm * 2018 - Master Of Arts * 2017 - Big Duke * 2016 - Libran * 2015 - Permit *2014 - The Offer *2013 - Julienas *2012 - Permit *2011 - Bid Spotter *2010 - Precedence *2009 - Enzedex Eagle *2008 - The Chieftain *2007 - The Chieftain *2006 - Fooram *2005 - Mahtoum *2004 - Saturday Fever *2003 - Grand City *2002 - Manner Hill *2001 - Tiger's Eye *2000 - Pravda *1999 - Our Unicorn *1998 - Praise Indeed *1997 - Palos Verdes *1996 - Tennessee Oak *1995 - Super Monarch *1994 - Air Seattle *1993 - Azzaam *1992 - Dr Grace *1991 - Dr Grace *1990 - Lord Hybrow *1989 - Concordance *1988 - Our Palliser *1987 - Indian Raj *1986 - Marooned *1985 - Astrolin *1984 - Hawaiian Rain *1983 - Kaidahom *1982 - Sean's Pride *1981 - Shamrock King *1980 - Shahman *1979 - Mr. Bluebeard *1978 - Cold Steel *1977 - Rhalif *1976 - Paris Court *1975 - Sovereign Yacht *1974 - Gala Supreme *1973 - Odyssey ==See also== * List of Australian Group races * Group races == External links == *First three placegetters N.E. Manion Cup ==References== Category:Horse races in Australia
N Force was a small New Zealand Army unit of infantry and artillery that garrisoned the Australian territory of Norfolk Island between October 1942 and February 1944, during the Second World War. The island was considered strategically important due to the cable station there that linked Australia and New Zealand. N Force was formed by detaching units from the 3rd New Zealand Division. An airfield was also constructed that was manned by Royal New Zealand Air Force (RNZAF) personnel. At its peak in October 1942, N Force consisted of 1,488 New Zealanders under the command of Lieutenant-Colonel J. W. Barry. At this time N-Force consisted of: * 36th Battalion (Infantry) * 152nd Heavy Battery (four 155mm guns) * Independent Field Artillery Troop (four 25 pounder guns) * 215th Composite Anti-Aircraft Battery (four 3.7-inch anti-aircraft and eight 40-millimetre guns) * Engineer, Army Service Corps and Ordnance detachments The 36th Battalion left Norfolk Island to rejoin the 3rd New Zealand Division on New Caledonia at the end of March 1943. The battalion was replaced by the 2nd Battalion, Wellington-West Coast Regiment. Meanwhile, the strength of N Force was subsequently reduced, and in February 1944 responsibility for Norfolk Island was taken over by the RNZAF. The last New Zealand forces were withdrawn from Norfolk Island in July 1946. ==Notes== ==References== * * ==External links== *NZ Artillery of World War 2 in the Pacific – Royal New Zealand Artillery Old Comrades' Association *The Army Service Corps (NZ) on Norfolk Island *The 36th on Norfolk Island (Chapter 4) Category:Military units and formations of New Zealand in World War II Category:Military history of New Zealand during World War II Category:Military history of Australia during World War II Category:History of Norfolk Island Category:Australia–New Zealand military relations
N Gokulakrishnan is a politician. He was a Member of Parliament, representing Puducherry in the Rajya Sabha (the upper house of India's Parliament).He was elected as the term of P. Kannan of INC end on 6 October 2015. He belongs to the Indian All India Anna Dravida Munnetra Kazhagam (ADMK) political party. ==References== Category:1958 births Category: Living people Category: All India Anna Dravida Munnetra Kazhagam politicians Category: Rajya Sabha members from Puducherry Category: Puducherry politicians
N II U (pronounced "Into You") is an R&B; group from New Jersey consisting of Chuckie Howard, Chris Herbert, Don Carlis and Craig Hill. The group's only pop hit was the single "I Miss You", which peaked at #22 on the Billboard Hot 100 in 1994. ==Discography== ===Albums=== * N II U (1994) ===Singles=== Year Song U.S. Hot 100 U.S. R&B; U.S. Rhythmic Album 1994 "You Don't Have to Cry" - 56 - N II U 1994 "I Miss You" 22 14 9 N II U 1995 "There Will Never Be" - 90 - N II U ==Notes== * ==References== ==External links== * Category:American contemporary R&B; musical groups