Quark-hadron continuity under rotation:vortex continuity or boojum?
2018/8/30@RIKEN

Muneto Nitta(新田宗土)
Chandrasekhar Chatterjee, Shigehiro Yasui(安井 繁宏)
Keio U.(慶應義塾大学)

Topic in this talkfrom Fukushima & Hatsuda
Rept.Prog.Phys. 74 (2011) 014001

Quantum Chromo Dynamics (QCD)
quarksQuark matteri i = u,d,s flavor(global) SU(3)q α = r,g,b color(gauge) SU(3)Color-flavor locked(CFL) phase“Color superconductor”@ high density
Bailin-Love(‘79),
Iwasaki-Iwado(‘95)
Alford-Rajagopal-Wilczek(‘98)

i =    ijk q q ~ 1ijk

3x3 matrix
from Fukushima & Hatsuda
Rept.Prog.Phys. 74 (2011) 014001

Color superconductivity
as well as superfluidity

Continuity of Quark and Hadron Matter
Thomas Schäfer and Frank Wilczek
Phys. Rev. Lett. 82, 3956 – Published 17 May 1999 (continuity or crossover)No phase transition between hadron and CFL phases
Matching of symmetries and excitations (Nambu-Goldstone modes etc)
Three-flavor quarks with degenerate massSuperfluid
vortices

Neutron Stars

NeutronCore Nuclear matter superfluid

Rotation

Magneticfield

Proton Baym&Pines (‘60s)
super- Anderson&Itoh (‘75) vortices
conductor(Flux tubes)

How do vortices connect?

???

Hadron(hyperon)matterQuark Matter(CFL)???

Continuity of Quark and Hadron Matter
Thomas Schäfer and Frank Wilczek
Phys. Rev. Lett. 82, 3956 – Published 17 May 1999
Colorful boojums at the interface of a color superconductor
Mattia Cipriani, Walter Vinci, and Muneto Nitta
Phys. Rev. D 86, 121704(R) – Published 21 December 2012
Continuity of vortices from the hadronic to thecolor-flavor locked phase in dense matter
Mark G. Alford, Gordon Baym, Kenji Fukushima,Tetsuo Hatsuda, Motoi Tachibana
e-Print: arXiv:1803.05115 [hep-ph]
Quark-hadron continuity under rotation: vortex continuity or boojum?
Chandrasekhar Chatterjee, Muneto Nitta, Shigehiro Yasui
e-Print: arXiv:1806.09291 [hep-ph]Anyonic particle-vortex statistics and the nature of dense quark matter
Aleksey Cherman, Srimoyee Sen, Laurence G. Yaffe
e-Print: arXiv:1808.04827 [hep-th]What is Boojum?

BoojumBoojum trees in Arizona

A particularly dangerous
kind of Snark“The HuntingOf Snark”
Lewis CarrollWhat is Boojum?
In physics, named byD.Mermin (1976)
Boojums on the container wallin superfluid 3He-A

Boojum inliquid crystal

Boojums in 3He A-B phaseboundary

Boojum in two component BECs
Kasamatsu-TakeuchiMN-Tsubota, JHEP1011:068,2010[arXiv:1002.4265]

Colorful boojum at interface of quark matter

Cipriani,Vinci & MN, Phys.Rev.D86:121704,2012 [arXiv:1208.5704]

Neutron boojum= Colorful boojum
Nuclearmatter

Quarkmatter
Cipriani,Vinci & MN, Phys.Rev.D86:121704,2012 [arXiv:1208.5704]

Color superconductori =    ijk q j qk

 = 1,2,3 ( r, g, b) i = 1,2,3 ( u, d, s) d[ g sb ] s[ g ub ] u[ g d b ]  r = gbi =  d[ b sr ] s[ bur ] u[ bd r ]  g = brd s
 b = rgsu
ud[r g ]  [r g ] [r g ]u = ds d = sb s = udi→egcolor i gflavor
G = U (1) B  SU (3)C  SU (3) Fi

Landau-Ginzburg model from QCDGLparameters

Iida&Baym(‘01)
Giannakis&Ren(‘02)
Iida,Matsuura,Tachibana&Hatsuda(‘04)

densityof state

For a while we consider high density limit, where strange quark mass can be neglected.
We also ignore E&M interaction. Later we take into account these.

Color superconductori =    ijk q j qk

 = 1,2,3 ( r, g, b) i = 1,2,3 ( u, d, s)Groundstate

00  r = gb i =  0
0  g = br 0
 b = rg0
color-flavor
locked (CFL) u = ds d = sb s = udG = U (1) B  SU (3)C  SU (3) F U (1) B superfluidity−1→ H = SU (3)C+ F gcolor = gflavor
SU (3)Ccolor superconductivity

Color superconductori =    ijk q j qk
Integerquantized
superfluidvortex

 = 1,2,3 ( r, g, b) i = 1,2,3 ( u, d, s) 1 ( r )ei
i = 00
u = ds01 ( r )ei0

 r = gb0
0
 g = bri 1 ( r )e  b = rg

d = sbs = ud

Iida & Baym, Forbes & Zhitnitsky(‘02)

Color superconductor

i =    ijk q j qk

 = 1,2,3 ( r, g, b) i = 1,2,3 ( u, d, s)
1/3 quantizedi(r)evortex 100  r = gbi = 0
0 (r)
0  g = br
 b = rg
00

(r)
0


u = ds d = sb s = ud

Balachandran, Digal & Matsuura (BDM) (‘05)
Nakano, MN & Matsuura (‘07), Eto & MN (‘09)

1/3 quantized vortex

 1 ( r )ei
i = 0
000 
0 (r)0 0 0 ( r ) 0  1 ( r )2 0i  i = exp  exp  0 − 1 0  03
 3
 000−1
1/3 quantized

F12 ~  rdASU(3) color
color flux tube00 0 (r)0 0 0 ( r ) Superfluid vortex
Non-Abelian vortex

1/3 quantized vortex

 1 ( r )ei
i = 0
0


00 

0 (r)0 0 0 ( r ) F  1 + 2 0 , trace

Profiles G  1 −  0 , traceless01Long tail ofa superfluid
vortexGauge field

Eto & MN (‘09)

confinedcolor flux

1/3 quantized vortex0 0 (r)i =  0
1 ( r )ei
 00


0 

0 
 0 ( r ) 00 
 − 1 0 0   0 ( r )i  i = exp  exp  0 2 0  0
1 ( r )
0 3
 3
 0

00
−10

(r)
0



1/3 quantized

F12 ~  rdASU(3) color
color flux tube

Superfluid vortex
Non-Abelian vortex

1/3 quantized vortex

00 0 (r)i =  0
0 (r)
0i  00
(r)
e1

00 
 − 1 0 0   0 ( r )i  i = exp  exp  0 − 1 0  0
0 (r)
0 3
 3
 0

0020

(r)
1



1/3 quantized

F12 ~  rdASU(3) color
color flux tube

Superfluid vortex
Non-Abelian vortex

Comment
1/3 quantized vortex
Non-Abelian vortices
00 0 (r) were discovered earlier in the context of
i =  0
0 (r)
0 Supersymmetry andi  00
(r)
e1

 String theory (‘03)

00  − 1 0 0   0 ( r )i  i = exp  exp  0 − 1 0  0
0 (r)
0 3
 3
 0

0020

(r)
1



1/3 quantized

F12 ~  rdASU(3) color
color flux tube

Superfluid vortex
Non-Abelian vortex

Non-Abelian vortices Color 1 ( r )e00 0 (r) 0
 0
i

00 

0 (r)0 0 0 ( r ) 01 ( r )ei
00 
0 
 0 ( r ) 00 0 (r)
0 (r)
0
 0
i 
 00

(r)
e1



FluxesAbelian vortex
No flux 1 ( r )ei
0

0


0
1 ( r )ei0Which areenergeticallyfavored?

0 0 
1 ( r )ei Non-Abelian vortices Color 1 ( r )e00
 0 (r) 0 0i

00 0 (r)0 0 0 ( r ) 01 ( r )ei0Fluxes

Abelian vortex
No flux0 0 
 0 ( r ) 00 0 (r)
0 (r)0
 0

i 
 00

(r)
e1



 1 ( r )ei
0


0


Split

E
= E
= E

0
1 ( r )ei0

 1
 = E
 90 
0 
1 ( r )ei Nakano, MN & Matsuura (‘07), simulation by Alford et.al (‘16)

Abrikosov vortex latticeColorful vortex lattice 1 ( r )ei
i = 0
0

H = SU (3)C+ F00 
0 (r)0  K = [ SU (2)  U (1)]C+ F
00 (r) @ vortex coreNambu-Goldstone modes localized around the vortex

HSU (3)C+ F
C = C= C  CP 2
KSU (2)  U (1)Continuous familyof solutions exists

Eto,Nakano&MN(’09)= Gapless modes propagating along the vortex line

“ground state”

1+1 dim effective theory

fluctuations

Effective theory of orientational modes Eto,Nakano&MN(’09)

HSU (3)C+ F== CP 2
K SU (2)  U (1) = ( ,  ,  )1

1+1 dim. world-sheet theory23

homogenouscoordinates† = 1
32

 0 (r)
 0
 0


0
0 (r)02 2

 1 ( r )ei
0

0


0

0

i 
1 ( r )e “toricdiagram”
SU ( 2)

Linear dispersion:
type I NG mode

SU ( 2)
SU (3)00 
0 (r)0 0 0 ( r ) SU ( 2)

 0 (r)

 0
 0
0
1 ( r )ei
00 
0 
 0 ( r ) Hadron matter with degenerate quark mass
⇒ Hyperon matter

Baryon: hyperon Λ=uds , Σ=uus, Ξ=ussΔΛ Λ =<Λ Λ> ≠ 08 x 8 = 1 + 8 + 8 + 10 + 10* + 27

U(1)B spontaneous symmetry breaking⇒ superfluidity⇒ vortices under rotation

How these ΛΛ vortices connect to non-Abelianvortices in CFL phase?

matchhadron phase

CFL phase

Bulk symmetries

Vortex core symmetries

Don’tmatch

H = SU (3)C+ F
SSB  vortex coreK = [ SU (2)  U (1)]C+ F
K = [ SU (2)  U (1)]C+ F

K = [ SU (2)  U (1)]C+ F

HSU (3)C+ F
2== CPK SU (2)  U (1)matchhadron phase

CFL phase

Bulk symmetries

Vortex core symmetries

SU(3)

Don’t
have tomatch

H = SU (3)C+ F
SSB  vortex coreK = [ SU (2)  U (1)]C+ F

K = [ SU (2)  U (1)]C+ F

K = [ SU (2)  U (1)]C+ F

HSU (3)C+ F
2== CPK SU (2)  U (1)Bogoliubov-de Gennes equation in hadron phaseΛ hyperon acquires a phase (1/2)×2π = π around a vortex
Λ=uds
At quark level…

Aharanov-Bohm(-like) phaseor holonomy

Aharanov-Bohm(-like) phase matching

Collaborators

Hadron, HEP, Cond-mat

Eiji Nakano（Kouchi）, Taeko Matsuura（Hokkaido）,
Minoru Eto（Yamagata）, Naoki Yamamoto（Keio）,
Shigehiro Yasui(Titech) , Kazunori Itakura（KEK),
Yuji Hirono（BNL）, Takuya Kanazawa(RIKEN),
Takanori Fujiwara(Ibaragi), Takahiro Fukui(Ibaragi),
Walter Vinci（USC）, Mattia Cipriani（Pisa）,
Michikazu Kobayashi（Kyoto）, Chandrasekhar Chatterjee (Keio)

[1] with Nakano,Matsuura,
Phys.Rev.D78:045002,2008 [arXiv:0708.4096][2] with Eto,
Phys.Rev.D80:125007,2009 [arXiv:0907.1278][3] with Eto,Nakano,Phys.Rev.D80:125011,2009 [arXiv:0908.4470][4] with Eto,Yamamoto,Phys.Rev.Lett.104:161601,2010 [arXiv:0912.1352][5] with Yasui,Itakura,Phys.Rev.D81:105003,2010 [arXiv:1001.3730][6] with Hirono,Kanazawa,Phys.Rev.D83:085018,2011 [arXiv:1012.6042][7] with Eto,Yamamoto,Phys.Rev.D83:085005,2011 [arXiv:1101.2574][8] with Fujiwara,Fukui,Yasui,Phys.Rev.D84:076002,2011 [arXiv:1105.2115][9] with Hirono,Phys.Rev.Lett.109:062501,2012 [arXiv:1203.5059][10] with Vinci,Cipriani,
Phys.Rev.D86:085018,2012 [arXiv:1206.3535][11] with Cipriani,Vinci,
Phys.Rev.D86:121704,2012 [arXiv:1208.5704][12] with Kobayashi,
PTEP:021B01,2014 [arXiv:1307.6632][13] with Eto,Hirono,Yasui, PTEP 2014 (2014) 012D01, invited review [arXiv:1308.1535][14] with Kobayashi,Nakano, JHEP 1406,130:2014 [arXiv:1311.2399][15] with Chatterjee,
Phys.Rev. D93: 065050, 2016 [arXiv:1512.06603][16] with Chatterjee, Cipriani, Phys. Rev. D 93, 065046 (2016) [arXiv:1602.01677][17] with Chatterjee,
Phys.Rev. D95 (2017) 085013 [arXiv:1612.09419]

Non-Abelian Statistics of Majorana fermions[18] with Yasui,Itakura,Phys.Rev.B83:134518,2011 [arXiv:1010.3331][19] with Yasui,Itakura,
Nucl.Phys.B859:261-268,2012 [arXiv:1109.2755][20] with Hirono,Yasui,Itakura,Phys.Rev.B86:014508,2012 [arXiv:1203.0173][21] with Yasui,Hirono,Itakura,Phys.Rev.E87:052142,2013 [arXiv:1204.1164]

Chiral symmetry breaking[22] with Shiiki[23] with Nakano,Matsuura,[24] with Eto,Nakano,[25] with Eto,Hirono,

Phys.Lett.B658:143-147,2008 [arXiv:0708.4091]
Phys.Lett.B672:61-64,2009 [arXiv:0708.4092]
Nucl.Phys.B821:129-150,2009 [arXiv:0903.1528]
PTEP 2014 (2014) 033B01 [arXiv:1309.4559]