String Model Building

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Savoy Hotel München I Amalienstraße 25 I 80333
München
String Model Building
Stuart Raby
String Pheno 09 Warsaw University June 19, 2009
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String Model Building or Searching for the MSSM

• Outline
• Random searches for the MSSM
• Virtues of SUSY GUTs
• Heterotic model building
• Smooth manifolds Free fermions
• Orbifolds
• F theory / Type IIB
• Heterotic - F theory duals
• Conclusion

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Random Searches for the MSSM
Type II intersecting D brane models


Gmeiner, Blumenhagen, Honecker, Lust Weigand
Gepner orientifolds
Anastasopoulos, Dijkstra, Kiritsis Schellekens
Heterotic free fermion landscape analysis
Dienes, Lennek, Senechal Wasnik
MSSM is quite rare !!
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Virtues of SUSY GUTs

• MZ ltlt MGUT Natural
• Explains charge quantization
• Predicts gauge coupling unification !!
• Predicts SUSY particles at LHC !
• Predicts proton decay
• Predicts Yukawa coupling unification
• w/Family symmetry Fermion mass
  hierarchy
• Neutrino masses and mixing via See-Saw
• LSP - Dark Matter candidate
• Baryogenesis via leptogenesis

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Standard Model
Where would you look ??
In this landscape ?
Or in a golf course ! GUT
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E8 x E8 Heterotic models
Smooth CY3 Free fermions Orbifold
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E8 x E8 Heterotic models Smooth CY3
Bouchard Donagi ( Cvetic)

SU(5) GUT
Wilson line breaking to SM gauge group
Higgs doublet triplet splitting
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E8 x E8 Heterotic models Smooth CY3

SM gauge group 3 families 1 or 2 pairs ( Hu
Hd )
R parity cons.
Function of moduli Need non-pert. physics
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E8 x E8 Heterotic models Free fermionic
Cleaver, Faraggi, Nanopoulos ( Walker) 1998

SM gauge group 3 families 1 pair ( Hu Hd )
Vector-like exotics decouple Non trivial Yukawa
matrices Neutrino See-Saw
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E8 x E8 Heterotic models Orbifolds

• Dixon, Harvey, Vafa Witten
• Font, Ibanez, kim, Nilles, Quevedo

• Kobayashi, Raby Zhang
• Buchmuller, Hamaguchi, Lebedev Ratz
• Lebedev, Nilles, Raby, Ramos-Sanchez, Ratz,
  
• Vaudrevange Wingerter
• Kim, Kim Kyae

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Mini-Landscape search LNRRRVW

• Models with 3 families, Higgs
• ONLY vector-like exotics
• Out of 30,000 models

Fertile patch in Heterotic landscape
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E8 x E8 heterotic string in 10D
Compactify 6D on (T2)3
Then mod by Z6-II (Z3 x Z2) and Add
Wilson lines
Z6 embedded in E8 x E8 gauge lattice as shift
V6 consistent with mod. inv. !
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Orbifold GUTs
First consider (T2)3/Z3 W3
Wilson line in
SU3 torus
Massless modes From Untwisted sector
(G2 , SU3) twisted sector
SU(6) GUT in 5 or 6D
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Then add Z2 orbifold W2
in long direction
P
( V2 )
P
( V2 W2 )
SU(6)
SU(5)
SU(3)xSU(2)xU(1)
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Two 4D fixed points are special !!
2 light families
Local SO(10) GUT
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2 (16) on SO(10) brane
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Third family Higgs in BULK
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Discrete non-Abelian Family symmetry
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S1/Z2

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161
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D4 family symmetry

geometry
space group sel. rule
doublet
singlets
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Fermion mass hierarchy

Natural Froggatt-Nielsen mechanism !
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Benchmark model

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Exact R-parity !!
U(1)B-L broken to Z2 matter parity

Forbids R-parity violating operators
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m term
m 0 in flat space SUSY limit

Yukawa couplings
Not realistic - yet
Neutrino masses via See-Saw
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Note Yukawa couplings, gauge couplings and
Vector-like exotic masses are functions of
moduli (along SUSY flat directions). Some of
these moduli are blow up modes for some, BUT NOT
ALL, of the orbifold fixed points.

2 fixed points are not blown up !!
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F theory / Type IIB models

• Beasley, Heckman Vafa
• Donagi Wijnholt
• Blumenhagen, Braun, Grimm Weigand
• Chen Chung
• Marsano, Saulina Schaefer-Nameki

• SU(5) GUT on D7 brane /
• Chiral matter in 6D /
• Yukawa couplings at triple intersectn
• of matter branes
• Fermion flavor hierarchy natural

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Gauge 7-brane /

Matter 7-brane /
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F theory / Type IIB models

• SU(5) breaks to SM gauge group
• with ltFYgt hypercharge flux
• Not possible in Heterotic string !
• ltFYgt on Higgs brane
• doublet-triplet splitting
• Spinor reps of SO(10) possible !
• Not possible in perturbative IIB

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F theory / Type IIB models

• Heckman Vafa
• Randall Simmons-Duffin

Due to flux in 2-3 surface breaking geometric
flavor symmetry
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Gravity decouples w/ non-compact z1
direction Local construction !

Blumenhagen, Braun, Grimm Weigand Marsano,
Saulina Schaefer-Nameki
global constructions
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E8 x E8 heterotic - F theory duality

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Work in progress

• We are now attempting to construct the F theory
  dual to our MSSM-like models.
• w/ Bobkov, Weigand Westphal
  
• Find more general description i.e. all
  models in the same universality class
• Provide a general understanding of moduli
  space
• Help understand moduli stabilization
  SUSY breaking ?

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Step 1 E8 x E8 heterotic orbifold on
smooth CY3 manifold ?
After first Z3 orbifold Wilson line W3 we
find 6D SU(6) orbifold GUT compactified on
(T2) 2 / Z3 x T2

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Complete spectrum of 6D orbifold GUT
Dundee, Raby Wingerter
Satisfies Gravity anomaly constraint
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Bershadsky, Intriligator, Kachru,
Morrison, Sadov Vafa hep-th/9605200
E8 x E8 heterotic on K3 x T2 w/instantons

E8 12 instantons in SU(3)xSU(2) ? SU(6)
(20 cc) 18 (6 c.c.) E8
12 instantons in E(6) higgsing?SO(8)
4 (8v 8s 8c
c.c.)
K3 instantons dual to T4 / Z3 orbifold
Wilson line !!
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Bershadsky, Intriligator, Kachru,
Morrison, Sadov Vafa hep-th/9605200
F-theory CY3 T2 fibration over Fn xT2 dual
to E8 x E8 heterotic K3 x T2 w/instantons

visible SU(6) 20 18 (6)
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Bulk gauge fields live in 8D matter fields
live in 6D
added fiber Z2 orb breaks N2 to N1

U1 flux breaks SU(6) to SU(5)
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Possible obstruction to finding F theory dual of
Heterotic orbifold model

• Need to keep two orbifold fixed points -
• Otherwise hypercharge gets mass
• Groot
  Nibbelink, Ha Trapletti
• Wilson line shrinks to point
• blow up modes on heterotic side leave
• 2 orbifold fixed points

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Wilson line in z3 breaks GUT to SM
Orbifold takes torus to sphere

Need orbifold fixed points !! Two light
families on D3 branes at fixed points ??
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Other model building considerations

• Gauge coupling unification
• Proton decay from dimension 5 6 ops.
• Supersymmetry breaking sparticle masses
• Heckman Vafa Aparicio, Cerdeno
  Ibanez
• Moduli stabilization
• Cosmological constant
• 10500 vacua ??
• Cosmology

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Conclusions
Important to test string theory
Several new ideas in string model building

Orbifold Local GUT MSSM
Global F theory constructions may open window
to general MSSM landscape
Final test at the LHC !