1. Title of talk1 A Fertile Patch in the Heterotic Landscape Stuart Raby Rutgers University March 24, 2009

2. Title of talk2 Kobayashi, Raby, Zhang hep-ph/0403065, hep-ph/040909 Buchmuller, Hamaguchi, Lebedev & Ratz hep-ph/0511035, hep-ph/0512326 Lebedev, Nilles, Raby, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter hep- th/0611095, hep-th/0611203, 0708.2691[hep-th] Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/0611020 Dundee, Raby & Wingerter arXiv:0805.4186 [hep-th] Dundee & Raby arXiv:0808.0992 [hep-th]

3. Title of talk3 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

4. Title of talk4 String Model Building  Orbifold GUTs  Local GUTs  3 = 2 + 1  “Benchmark” model Local SO(10) & SU(6) orbifold GUT Gauge-Higgs unification Y top = g GUT Exact R-parity Vector-like exotics & extra U(1)s decouple  i n SUSY limit D 4 family symmetry Gauge coupling unification & more …

5. Title of talk5 Constructing MSSM from heterotic string/ Caveats SUSY solution at M S 100’s moduli ( geometric & more ) moduli stabilization & SUSY breaking ?? save for later gauge & Yukawa couplings fcns. of moduli tune to desired values

6. 6 Standard Model = Where would you look ?? In this landscape ? Or in a golf course ! = GUT

7. Title of talk7  Perform focused search “Mini Landscape” Lebedev, Nilles, Raby, Ratz, Ramos-Sanchez, Vaudrevange & Wingerter  Use both Local & Orbifold GUTs  Find ~ 200 MSSM-like models  Consider properties of one “Benchmark” model See what MSSM-like means ! Outline

8. Title of talk8 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. !

9. Title of talk9 Untwisted T 1,5 twisted T 2,4 twisted T 3 twisted

10. Title of talk10 Mini-Landscape search Z 6 -II orbifold  V 6 breaks to SO(10) [or E(6)]  2 families [ 16 [or 27] ] in T 1 twisted sect. 1. Generate 2 Wilson lines W 3, W 2 2. Identify ‘inequivalent’ models 3. Select models with 4. Select models with 3 net (3,2) 5. Select models with non-anom. 6. Select models with 3 SM families + Higgses + vector-like exotics

11. Title of talk11 Mini-Landscape search LNRRRVW 218 Models with 3 families, Higgs & vector-like exotics

12. Title of talk12 Road to the MSSM with R-parity LNRRRVW – 0708.2691[hep-th] 1. Check for D = 0 directions 2. Check R parity 3. Check all exotics get large mass 4. Check light Higgs 5. Check charged fermion masses 6. Check neutrino masses 7. Check dimension 5 B & L violating ops.

13. Title of talk13 D = 0 D = 0 is not a significant constraint

14. Title of talk14 Generalized R parity Forbid Dim 2 & 3 operators Family Reflection symmetry or Matter parity

15. Title of talk15 Construct model w/ Generalized R parity Identify “suitable” B-L  standard for SM particles  vector-like on exotics  maximal no. SM singlets w/

16. Title of talk16 Results

17. Title of talk17 Gauge lattice Embed twist in gauge lattice via shift Wilson lines Benchmark Model

18. Title of talk18 Local SO(10) GUT Require massless SO(10) spinors at T 1 fixed points Mass operator

19. Title of talk19 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

20. Title of talk20 Consider massless Untwisted sector P 2 = 2 GSO projection Orbifold GUTs GaugeU3U3

21. Title of talk21 Gauge & U 3

22. Title of talk22 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 ) 2 light families

23. Title of talk23 2 (16) on SO(10) brane

24. Title of talk24 Third family & Higgs in BULK

25. Title of talk25 Discrete non-Abelian Family symmetry

26. Title of talk26 S 1 /Z 2 16 1 16 2

27. Title of talk27 D 4 family symmetry doubletsinglets geometryspace group sel. rule

28. Title of talk28 Fermion mass hierarchy

29. Title of talk29 Discrete Family Symmetries Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/0611020 See also: D 4 phenomenology Ko, Kobayashi, Park & Raby arXiv:0704.2807

30. Title of talk30 Benchmark model

31. Title of talk31 Exact R-parity !! U(1) B-L broken to Z 2 matter parity Forbids R-parity violating operators

32. Title of talk32  term  = 0 in flat space SUSY limit Yukawa couplings Neutrino masses via See-Saw Not realistic - yet

33. Title of talk33 Gauge coupling unification

34. Title of talk34 2 loop and weak scale corr’s KK modes exotics RG equations

35. Title of talk35 In this SU(6) orbifold GUT with gauge-Higgs unification the KK modes do NOT focus gauge couplings to unify at M string Therefore NEED exotics with mass M EX < M C

36. Title of talk36 Gauge coupling unification

37. Title of talk37 Proton Decay observable ?

38. Title of talk38 10D string coupling Dundee & Raby following Hebecker & Trapletti Weak Coupling !!

39. Title of talk39 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 Obtaining the same theory by compactifying E 8 x E 8 heterotic string on ‘smooth’ CY 3 manifold ?

40. Title of talk40 Satisfies Gravity anomaly constraint Complete spectrum of 6D SU(6) orbifold GUT

41. Title of talk41 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 !! 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

42. Title of talk42 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa

43. Title of talk43 Derivable from a dual F theory construction ?? 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 ?

44. Title of talk44 Conclusions We find MSSM in “fertile” patch of E(8)xE(8) heterotic string Important to test string theory SUSY breaking and lifting flat directions ?? Almost realistic “Benchmark” models !!! w/ Caveat Orbifold & Local GUT MSSM Derivable from F theory dual ??