2. Title of talk1 The Heterotic Road to the MSSM Stuart Raby Seoul National University June 10, 2008

3. Phenomenology  charge quantizationcharge quantization  gauge coupling unification  Yukawa unification  neutrino masses

4. Title of talk3 Pati-Salam SU(4) C xSU(2) L xSU(2) R

5. 4 Cartan-Weyl

6. Title of talk5 spinor repsn. of SO( 10 ) Charge quantization

7. Title of talk6 Phenomenology  charge quantization  gauge coupling unificationgauge coupling unification  Yukawa unification  neutrino masses

8. Title of talk7 Gauge coupling unification

9. Title of talk8 Phenomenology  charge quantization  gauge coupling unification  Yukawa unificationYukawa unification  neutrino masses

10. Title of talk9 Yukawa unification

11. Title of talk10 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino massesneutrino masses

12. Title of talk11 neutrino masses

13. Title of talk12 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino masses SO(10) SUSY GUT w/ L.E. SUSY

14. Title of talk13 Quark & Lepton masses and mixing Hierarchical Flavor symmetry breaking

15. Title of talk14 SUSY flavor problem ~ 125 soft SUSY breaking parameters ! FCNC Solutions 1. heavy 1 st & 2 nd generation scalars 2. degenerate squarks & sleptons at M G 3. alignment of fermions/sfermions 2 & 3 non-Abelian flavor sym.

16. Title of talk15 Phenomenology ( summary ) SO(10) SUSY GUT w/ L.E. SUSY & Discrete non-Abelian flavor symmetry

17. Title of talk16 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

18. Title of talk17 4 D GUT problems GUT symmetry breaking Higgs doublet – triplet splitting Solution ? Orbifold GUTs

19. Title of talk18 M 4 x S 1 /(Z 2 xZ 2 ’) P P’ P & P’ parity affect boundary conditions at fixed points

20. Orbifold SUSY GUTs in 5 or 6D  N=2  N=1 SUSY  chiral gauge theory  gauge symmetry breaking  Higgs doublet-triplet splitting All this first observed in heterotic string in 10D

21. Title of talk20 Outline  Orbifold GUTs / String Orbifolds Kobayashi, SR, Zhang hep-ph/0403065, hep-ph/0409098  Mini-Landscape : search for MSSM Lebedev et al hep-th/0611095, hep-th/0611203  Road to the MSSM with R-parity Lebedev et al – 0708.2691[hep-th]

22. Title of talk21 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

23. Title of talk22 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. !

24. Title of talk23 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 E 6 GUT in 5 or 6D

25. Title of talk24 Massless Untwisted sector P 2 = 2 GSO Gauge lattice

26. Title of talk25 E(6) x SU(3) Gauge & U 3

27. Title of talk26 Then add Z 2 orbifold + W 2 [in long direction] E6E6 SO(10)SU(4)xSU(2) L xSU(2) R F 3 = (4,2,1), F 3 c = (4 c,1,2), H = (1,2,2) PP’ ( V 2 )( V 2 + W 2 )

28. Title of talk27 T 1 twisted sector 2 Light fam’s Local GUT SO(10)

29. Title of talk28 S 1 /Z 2 16 1 16 2

30. Title of talk29 D 4 family symmetry doubletsinglets geometryspace group sel. rule

31. Title of talk30 Fermion mass hierarchy

32. Title of talk31 Discrete Family Symmetries Kobayashi, Nilles, Ploeger, SR & Ratz hep-ph/0611020 See also: D 4 phenomenology Ko, Kobayashi, Park & SR arXiv:0704.2807

33. Title of talk32 T 1 twisted sector Vector-like exotics Can get large mass & decouple !!

34. Title of talk33  3 rd family in bulkgauge-Yukawa unification  1 st and 2 nd families on Z 2 fixed points D 4 family symmetry  Higgs for PS symmetry breaking To summarize

35. Title of talk34 Mini-Landscape search hep-th/0611095 Lebedev, Nilles, SR, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter Search for MSSM Spectra in heterotic orbifolds

36. Title of talk35 Follow lead of Buchmuller, Hamaguchi, Lebedev & Ratz using same Z 6 -II orbifold hep-ph/0511035, hep-ph/0512326 Looked for and found SM gauge group in 4D with 3 families and vector-like exotics

37. Title of talk36 Mini-Landscape search Z 6 -II orbifold 1. V 6 breaks to SO(10) [or E(6)] 2. 2 families [ 16 [or 27] ] in T 1 twisted sect. 3. Generate 2 Wilson lines W 3, W 2 4. Identify ‘inequivalent’ models 5. Select models with 6. Select models with 3 net (3,2) 7. Select models with non-anom. 8. Select models with 3 SM families + Higgses + vector-like exotics

38. Title of talk37 Mini-Landscape search LNRRRVW

39. Title of talk38 Mini-Landscape search LNRRRVW 93 MSSM-like models or probability ~ 1/300 “Fertile” patch in heterotic landscape !! w/ Arbitrary singlet VEVs

40. Title of talk39 Supersymmetry Breaking

41. Title of talk40 Low Energy SUSY Breaking LNRRRVW New step 8 : 77 models

42. Title of talk41 Number of models vs. the size of largest gauge group in the hidden sector. N labels SU(N), SO(2N), E(N) groups. The background corresponds to Step 2, while the foreground corresponds to Step 8. The background corresponds to Step 2, while the foreground corresponds to Step 6.

43. Title of talk42 Gluino condensate Assume stabilize S in Kahler potential & take

44. Title of talk43 Number of models vs. scale of gaugino condensation.

45. Title of talk44 GUTs or String Unification ??

46. Title of talk45 GUTs or String Unification ? S.R. & Wingerter 0706:0217 [hep-th] New search - Remove restrictions  on SU(3)xSU(2) in SU(5) n hypercharge in SU(5) Now find

47. Title of talk46 ML: 1170 ML: 127

48. Title of talk47 Sin 2  90% in SU(5) Only ~ 12 % w/ Sin 2  1220 models

49. Title of talk48 Road to the MSSM with R-parity LNRRRVW – 0708.2691[hep-th] 1. Check for D = 0 directions 2. Check all exotics get large mass 3. Check R parity 4. Check light Higgs 5. Check charged fermion masses 6. Check neutrino masses 7. Check dimension 5 B & L violating ops.

50. Title of talk49 Results Not significant constraint !!

51. Title of talk50 Generalized R parity Forbid Dim 2 & 3 operators Family Reflection symmetry or Matter parity

52. Title of talk51 Construct model w/ Generalized R parity Identify “suitable” B-L  standard for SM particles  vector-like on exotics  maximal no. SM singlets w/

53. Title of talk52 Results

54. Title of talk53 Results

55. Title of talk54 Consider One “Benchmark” Model G = SU(3)xSU(2)x [SU(4)xSU(2)’]xU(1) 9 1. Spectrum 2.  term 3. Yukawa couplings 4. Neutrino masses 5. Dim. 5 ops.

56. Title of talk55 OOrbifold GUT - SU(6) LLocal GUT - SO(10) x SO(4)

57. Title of talk56 Spectrum

58. Title of talk57  term  ~ M Z Yukawa couplings Not realistic - YET

59. Title of talk58 Neutrino masses via See-Saw YES !! Dimension 5 operators – suppressed ~ BUT generated again when integrating out  s tates - problem ??

60. Title of talk59 Gauge coupling unification Dundee, Raby & Wingerter arXiv:0805.4186 [hep-th]

61. Title of talk60 Gauge coupling unification

62. Title of talk61 Proton Decay Dundee, Raby & Wingerter arXiv:0805.4186 [hep-th]

63. Title of talk62 Proton lifetime too short observable

64. Title of talk63 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