Savoy Hotel Mnchen I Amalienstrae 25 I 80333

Savoy Hotel München I Amalienstraße 25 I 80333 München String Model Building Stuart Raby String Pheno 09 Warsaw University June 19, 2009 Title of talk 1

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 Title of talk 2

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 !! Title of talk 3

Virtues of SUSY GUTs § § § § § MZ << 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 Title of talk 4

Standard Model = Where would you look ? ? In this landscape ? Or in a golf course ! = GUT Title of talk 5

E 8 x E 8 Heterotic models Smooth CY 3 Free fermions Orbifold Title of talk 6

E 8 x E 8 Heterotic models Smooth CY 3 Bouchard & Donagi ( & Cvetic) SU(5) GUT Wilson line breaking to SM gauge group Higgs doublet – triplet splitting Title of talk 7

E 8 x E 8 Heterotic models Smooth CY 3 SM gauge group 3 families 1 or 2 pairs ( Hu + Hd ) R parity cons. Function of moduli Need non-pert. physics Title of talk 8

E 8 x E 8 Heterotic models Free fermionic SM gauge group 3 families 1 pair ( Hu + Hd ) Cleaver, Faraggi, Nanopoulos (& Walker) 1998 Vector-like exotics decouple Non trivial Yukawa matrices & Neutrino See-Saw Title of talk 9

E 8 x E 8 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 § Title of talk 10

Mini-Landscape search LNRRRVW 223 Models with 3 families, Higgs & ONLY vector-like exotics Out of ~ 30, 000 models Fertile patch in Heterotic landscape Title of talk 11

E 8 x E 8 heterotic string in 10 D Compactify 6 D on (T 2)3 Then mod by Z 6 -II = (Z 3 x Z 2) and Add Wilson lines Z 6 embedded in E 8 x E 8 gauge lattice as shift V 6 : consistent with mod. inv. ! Title of talk 12

Orbifold GUTs First consider (T 2)3/Z 3 + W 3 [Wilson line in SU 3 torus] Massless modes From Untwisted sector + (G 2 , SU 3) twisted sector Title of talk SU(6) GUT in 5 or 6 D 13

Then add Z 2 orbifold + W 2 [in long direction] P ( V 2 ) SU(6) P’ ( V 2+ W 2 ) SU(5) SU(3)x. SU(2)x. U(1) Title of talk 14

Two 4 D fixed points are special !! Local SO(10) GUT Title of talk 2 light families 15

2 (16) on SO(10) brane Title of talk 16

Third family & Higgs in BULK Title of talk 17

Discrete non-Abelian Family symmetry Title of talk 18

S 1/Z 2 161 Title of talk 19

D 4 family symmetry geometry space group sel. rule doublet singlets Title of talk 20

Fermion mass hierarchy Natural Froggatt-Nielsen mechanism ! Title of talk 21

Benchmark model Title of talk 22

Exact R-parity !! U(1)B-L broken to Z 2 matter parity Forbids R-parity violating operators Title of talk 23

m term m = 0 in flat space SUSY limit Yukawa couplings Not realistic - yet Neutrino masses via See-Saw Title of talk 24

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 !! Title of talk 25

F theory / Type IIB models § § § Beasley, Heckman & Vafa Donagi & Wijnholt Blumenhagen, Braun, Grimm & Weigand Chen & Chung Marsano, Saulina & Schaefer-Nameki • SU(5) GUT on D 7 brane / • Chiral matter in 6 D / • Yukawa couplings at triple intersect’n of matter branes – • Fermion flavor hierarchy natural Title of talk 26

Gauge 7 -brane / Matter 7 -brane / Title of talk 27

F theory / Type IIB models • SU(5) breaks to SM gauge group with <FY> : hypercharge flux Not possible in Heterotic string ! • • <FY> on Higgs brane doublet-triplet splitting Spinor reps of SO(10) possible ! Not possible in perturbative IIB Title of talk 28

F theory / Type IIB models § § Heckman & Vafa Randall & Simmons-Duffin Due to flux in 2 -3 surface breaking geometric flavor symmetry Title of talk 29

Gravity decouples w/ non-compact z 1 direction Local construction ! Blumenhagen, Braun, Grimm & Weigand global constructions Marsano, Saulina & Schaefer-Nameki Title of talk 30

E 8 x E 8 heterotic - F theory duality Title of talk 31

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 ? § Title of talk 32

Step 1: E 8 x E 8 heterotic orbifold on ‘smooth’ CY 3 manifold ? After first Z 3 orbifold + Wilson line W 3 we find 6 D SU(6) orbifold GUT compactified on (T 2) 2 / Z 3 x T 2 Title of talk 33

Complete spectrum of 6 D orbifold GUT Dundee, Raby & Wingerter Satisfies Gravity anomaly constraint Title of talk 34

Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 E 8 x E 8 heterotic on K 3 x T 2 w/instantons E 8 [12 instantons in SU(3)x. SU(2)] SU(6) + (20 + cc) + 18 (6 + c. c. ) E 8 [12 instantons in E(6) + higgsing] SO(8) + 4 (8 v+ 8 s+ 8 c + c. c. ) K 3 + instantons dual to T 4 / Z 3 orbifold + Wilson line !! Title of talk 35

Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 F-theory CY 3 [T 2 fibration over Fn] x. T 2 dual to E 8 x E 8 heterotic K 3 x T 2 w/instantons visible SU(6) 20 + 18 (6) Title of talk 36

Bulk gauge fields live in 8 D & matter fields live in 6 D added fiber & Z 2 orb… breaks N=2 to N=1 U 1 flux breaks SU(6) to SU(5) Title of talk 37

Possible obstruction to finding F theory dual of Heterotic orbifold model Need to keep two orbifold fixed points 1. Otherwise hypercharge gets mass 2. 3. Groot Nibbelink, Ha & Trapletti Wilson line shrinks to point blow up modes on heterotic side leave 2 orbifold fixed points Title of talk 38

Orbifold takes torus to sphere Wilson line in z 3 breaks GUT to SM Need orbifold fixed points !! Two light families on D 3 branes at fixed points ? ? Title of talk 39

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 Title of talk 40

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 ! Title of talk 41