# Presentation: 176117

##              Constructing 5D Orbifold GUTs 

-              Constructing 5D Orbifold GUTs
-                    from Heterotic Strings

- w/ R.J. Zhang and T. Kobayashi
-            Phys. Lett.  B593, 262 (2004) &
-            Nucl. Phys. B704, 3 (2005)
- w/ A. Wingerter and P. Vaudrevange,  in progress

- Fermilab  Theory Seminar

- Stuart Raby

- May 25, 2006

- Title of talk

##        In 2007,  the LHC turns on; hopefully opening up a new age of discovery.   String theory is by far the best candidate for a self-consistent quantum theory of gravity. Moreover,  it provides a framework for a true theory of everything.

-        In 2007,  the LHC turns on; hopefully opening up a new age of discovery.   String theory is by far the best candidate for a self-consistent quantum theory of gravity. Moreover,  it provides a framework for a true theory of everything.
-       Estimates suggest there are more than 10300         string vacua.  The string vacuum fixes the gauge   group, the number of families, fermion masses and   supersymmetry breaking.  Many have searched for
-     phenomenologically acceptable string vacua.
-    Yet we do not know whether even one string vacuum exists which looks like the real world.
-         This talk describes a new search in an old direction -- the weakly coupled heterotic string.
-         Our results are promising;  already providing some interesting new models.   We are guided in our approach by recent progress in understanding model
-     building in 5 and 6 dimensional orbifold SUSY GUT field theories.

- Title of talk

##     Use intuition from Orbifold GUTs

-        Phenomenological Guidelines

-   Preserve gauge coupling unification
-   Low energy SUSY                MZ << MG
-   Quarks and leptons in 16 of SO(10)
-   Higgs in 10
-   Preserve GUT relations for 3rd family Yukawa
-   “Natural”  See-Saw scale  ~ MG
-     _Use intuition from Orbifold GUTs_

- Title of talk

## Consider  E6  example

-        Outline

- 3  Family Orbifold GUT on   **M****4**** x S****1****/(Z****2****xZ****2****’)**

- Heterotic string compactified on  **[T****2****]****3****/Z****6**
-    +  Wilson  lines

- Consider  E6  example

- Title of talk

## Slide 5

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## Slide 6

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## Slide 7

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## E6   Orbifold GUT  on  M4 x S1/(Z2xZ2’)

- E6   Orbifold GUT  on  **M****4**** x S****1****/(Z****2****xZ****2****’)**

- Title of talk

## E8 x E8   Heterotic  string  in  10D

- E8 x E8   Heterotic  string  in  10D

- Compactify  6D   on  (T2)3

- Then  mod by Z6 =  (Z3 x Z2)  and
- Add  Wilson lines

- Z6  embedded in  E8 x E8  gauge lattice
- as  shift  V6 :  consistent with mod. inv. !

- Title of talk

##    First consider   (T2)3/Z3    +   W3                

-    _First consider _  (T2)3/Z3    +   W3
-                           [Wilson line in  SU3 torus]

- Massless   modes
- From Untwisted sector   +
- (G2 , SU3)   twisted sector

- E6 GUT
-  in 5D

- Title of talk

## E6   

-            Then add  Z2  orbifold  +   W2
-                   [in long direction]

- E6

- SO(10)

- SU(4)xSU(2)LxSU(2)R

- F3 = (4,2,1),   F3c = (4c,1,2) ,  H = (1,2,2)

- P

- P’

-  ( V2 )

- ( V2+ W2 )

- Title of talk

## D4   family symmetry !!

-       Two families sit on  Z2  fixed points !!

- D4   family symmetry !!

- Exotics

- Title of talk

##   D4  family symmetry 

-   D4  family symmetry

- doublet

- singlet

- Title of talk

## Z2   twisted sector

-          Extra  color triplets  !!

- Z2   twisted sector

- Title of talk

## E6   Orbifold GUT  on  M4 x S1/(Z2xZ2’)

- E6   Orbifold GUT  on  **M****4**** x S****1****/(Z****2****xZ****2****’)**

- Title of talk

## To summarize

-    3rd  family in bulk

- gauge-Yukawa unification

-    1st and 2nd families  on Z2 fixed points

- D4 family symmetry

- Higgs for PS   symmetry breaking

- Title of talk

## F and D flat direction breaks

- _PS  symmetry breaking_

- PS to SM
- +  gives mass to all SM non-singlets

- Title of talk

## Gauge coupling unification ?

- _Gauge coupling unification ?_

- 4D  GUT

- 5D  Orbifold GUT

- Title of talk

## Gauge coupling unification

- _Gauge coupling unification_

- ++  and  --  modes are in overlap of

- and

- Title of talk

## Weak

- B.C.s

- Strong

- Title of talk

## Successes

- _Successes_

-   3rd generation  and  Higgs  in bulk
-      ->        gauge-Yukawa unif.

-   D4  family symmetry :  family hierarchy
-     +  suppress flavor violation

-   Gauge coupling unification

- Title of talk

## D4   family symmetry

- D4   family symmetry

- Title of talk

## So what’s the problem ?

- _So what’s the problem ?_

-       Exotics

- So  what  now  ?
-    Search  for  R  parity  inv.  theory
-    Z3 x Z2  or  Alternate  orbifold construct

-        NO   _R  parity_     !!

- BUT      Vector-like

- May  be  OK ?

- OK !  IF massive

- Title of talk

## New Search   Z2 x Z4  orbifold  

- New Search   Z2 x Z4  orbifold

-        V2 x V4        120  inequivalent possibilities
-  W1  and/or  W2           500,000   possible  models

- Narrow  the  search

- Consider  eg.   MSSM  in  4D
-                                      Why bother with GUTs  
- Demand -
-        3 ( 3, 2 )  +  6 ( 3* , 1 )  +  > 5  ( 1 , 2 )
-        TYPICALLY  have  Chiral Exotics
-                               i.e.   Wrong  Hypercharge   

- w/ Wingerter & Vaudrevange

- Title of talk

## Solution -  Demand   PS   or   SU(5) 

- Solution -  Demand   PS   or   SU(5)
- intermediate sym.  &  identify hypercharge
-  1⁄2 ( B – L) + T3R  in  PS  or  Y in SU(5)

-      MSSM  in  4D
-             w/ 3 families  &  NO  chiral exotics
-         Find    PS   ->  SM  -   6  models
-                 SU(5) ->  SM -  40  models
- II.     Pati – Salam in  4D
-            w/ 3 families,  PS  Higgs
-                  &  NO chiral exotics
-          Find  ~    220   models

- Title of talk

## Z2 x Z4  orbifold  construction

- One  example :  preliminary

- Part of third family in bulk =>  heavy top

- Two light families on  (0,1)  fixed poiints

- Title of talk

## Spectrum

- _Spectrum_

- Order  S0 :  top mass
-           S2  :  bottom +  tau mass
-                     term

- Title of talk

## Conclusions

- _Conclusions_

-   New  3 family E6 orbifold GUT
-   3rd generation  -- gauge-Yukawa unif.
-   D4  family symmetry :  family hierarchy
-     +  suppress flavor violation
-   Few  _vector-like_  exotics
-    NO   _R  parity  _   

-  Z2 x Z4    &    Z2 x Z3      search in progress

- Title of talk