1. Title of talk1 String Model Building Stuart Raby String Pheno 09 Warsaw University June 19, 2009 Savoy Hotel M ü nchen I Amalienstra ß e 25 I 80333 M ü nchen

2. Title of talk2 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 String Model Building or Searching for the MSSM

3. Title of talk3 Random Searches for the MSSM Type II intersecting D brane models Gepner orientifolds Heterotic free fermion landscape analysis Gmeiner, Blumenhagen, Honecker, Lust & Weigand Anastasopoulos, Dijkstra, Kiritsis & Schellekens Dienes, Lennek, Senechal & Wasnik MSSM is quite rare !!

4. Title of talk4 Virtues of SUSY GUTs  M Z << M GUT “Natural”  Explains charge quantization  Predicts gauge coupling unification !! redicts SUSY particles at LHC ! redicts proton decay redicts Yukawa coupling unification  w/Family symmetry Fermion mass hierarchy  Neutrino masses and mixing via See-Saw  LSP - Dark Matter candidate  Baryogenesis via leptogenesis

5. Title of talk5 Standard Model = Where would you look ?? In this landscape ? Or in a golf course ! = GUT

6. Title of talk6 E 8 x E 8 Heterotic models Smooth CY 3 Free fermions Orbifold

7. Title of talk7 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

8. Title of talk8 E 8 x E 8 Heterotic models Smooth CY 3 SM gauge group 3 families 1 or 2 pairs ( H u + H d ) R parity cons. Function of moduli Need non-pert. physics

9. Title of talk9 E 8 x E 8 Heterotic models Free fermionic SM gauge group 3 families 1 pair ( H u + H d ) Cleaver, Faraggi, Nanopoulos (& Walker) 1998 Vector-like exotics decouple Non trivial Yukawa matrices & Neutrino See-Saw

10. Title of talk10 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

11. Title of talk11 Mini-Landscape search LNRRRVW 223 Models with 3 families, Higgs & ONLY vector-like exotics Out of ~ 30,000 models Fertile patch in Heterotic landscape

12. Title of talk12 E 8 x E 8 heterotic string in 10D Compactify 6D 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. !

13. Title of talk13 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 SU(6) GUT in 5 or 6D Orbifold GUTs

14. Title of talk14 Then add Z 2 orbifold + W 2 [in long direction] SU(6) SU(5)SU(3)xSU(2)xU(1) P P’P’ ( V 2 ) ( V 2 + W 2 )

15. Title of talk15 Local SO(10) GUT 2 light families Two 4D fixed points are special !!

16. Title of talk16 2 (16) on SO(10) brane

17. Title of talk17 Third family & Higgs in BULK

18. Title of talk18 Discrete non-Abelian Family symmetry

19. Title of talk19 S 1 /Z 2 16 1 16 2

20. Title of talk20 D 4 family symmetry doubletsinglets geometryspace group sel. rule

21. Title of talk21 Fermion mass hierarchy Natural Froggatt-Nielsen mechanism !

22. Title of talk22 Benchmark model

23. Title of talk23 Exact R-parity !! U(1) B-L broken to Z 2 matter parity Forbids R-parity violating operators

24. Title of talk24  term  = 0 in flat space SUSY limit Yukawa couplings Neutrino masses via See-Saw Not realistic - yet

25. Title of talk25 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 !!

26. Title of talk26 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 intersect’n of matter branes – Fermion flavor hierarchy natural

27. Title of talk27 Gauge 7-brane / Matter 7-brane /

28. Title of talk28 F theory / Type IIB models SU(5) breaks to SM gauge group with <F Y > : hypercharge flux Not possible in Heterotic string ! <F Y > on Higgs brane doublet-triplet splitting Spinor reps of SO(10) possible ! Not possible in perturbative IIB

29. Title of talk29 F theory / Type IIB models  Heckman & Vafa  Randall & Simmons-Duffin Due to flux in 2-3 surface breaking geometric flavor symmetry

30. Title of talk30 Gravity decouples w/ non-compact z 1 direction Local construction ! Blumenhagen, Braun, Grimm & Weigand Marsano, Saulina & Schaefer- Nameki global constructions

31. Title of talk31 E 8 x E 8 heterotic - F theory duality

32. Title of talk32 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 ?

33. Title of talk33 After first Z 3 orbifold + Wilson line W 3 we find 6D SU(6) orbifold GUT compactified on (T 2 ) 2 / Z 3 x T 2 Step 1: E 8 x E 8 heterotic orbifold on ‘smooth’ CY 3 manifold ?

34. Title of talk34 Satisfies Gravity anomaly constraint Complete spectrum of 6D orbifold GUT Dundee, Raby & Wingerter

35. Title of talk35 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 E 8 [12 instantons in SU(3)xSU(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 !! E 8 x E 8 heterotic on K 3 x T 2 w/instantons

36. Title of talk36 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 F-theory CY 3 [T 2 fibration over F n ] xT 2 dual to E 8 x E 8 heterotic K 3 x T 2 w/instantons visible SU(6) 20 + 18 (6)

37. Title of talk37 Bulk gauge fields live in 8D & matter fields live in 6D U 1 flux breaks SU(6) to SU(5) added fiber & Z 2 orb… breaks N=2 to N=1

38. Title of talk38 Possible obstruction to finding F theory dual of Heterotic orbifold model Need to keep two orbifold fixed points - 1. Otherwise hypercharge gets mass Groot Nibbelink, Ha & Trapletti 2. Wilson line shrinks to point 3. blow up modes on heterotic side leave 2 orbifold fixed points

39. Title of talk39 Need orbifold fixed points !! Two light families on D3 branes at fixed points ?? Wilson line in z 3 breaks GUT to SM Orbifold takes torus to sphere

40. Title of talk40 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 10 500 vacua ?? Cosmology

41. Title of talk41 Conclusions Several new ideas in string model building Important to test string theory Global F theory constructions may open window to general MSSM landscape Orbifold & Local GUT MSSM Final test at the LHC !