2. Title of talk1 Unification & B-L in String Theory Stuart Raby B-L Workshop, LBL September 21, 2007

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

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 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino masses

11. Title of talk10 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino masses SO(10) SUSY GUT w/ L.E. SUSY M See-Saw ~ (.01 -.1) M G

12. Title of talk11 4 D GUT problems GUT symmetry breaking Higgs doublet – triplet splitting Solution ? Orbifold GUTs

13. Title of talk12 M 4 x S 1 /(Z 2 xZ 2 ’) P P’ P & P’ parity affect boundary conditions at fixed points

14. Orbifold SUSY GUTs in 5 or 6D P & P’ boundary conditions can  break N=2  N=1 SUSY  give chiral gauge theory auge symmetry breaking  Higgs doublet-triplet splitting All this first observed in heterotic string in 10D

15. Title of talk14 Outline  Orbifold GUTs / String Orbifolds Kobayashi, SR, Zhang hep-ph/0403065, hep-ph/0409098  Mini-Landscape : search for MSSM LNR 3 VW hep-th/0611095, hep-th/0611203  Road to the MSSM w/ R-parity LNR 3 VW 0708.2691 [hep-th]

16. Title of talk15 E 8 x E 8 heterotic string Constructing MSSM / 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

17. Title of talk16 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. !

18. Title of talk17 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

19. Title of talk18 E 6 Orbifold GUT on M 4 x S 1 /(Z 2 xZ 2 ’)

20. Title of talk19 Then add Z 2 orbifold + W 2 [Wilson Line] [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 )

21. Title of talk20 T 1 twisted sector 2 Light fam’s Vector-like exotics Local GUT SO(10)

22. Title of talk21 E 6 Orbifold GUT on M 4 x S 1 /(Z 2 xZ 2 ’)

23. Title of talk22 Advantage of Orbifold & Local GUTs 1. Local SO(10) GUT with 16s at fixed points guarantees charge quantization 2. Orbifold GUT with SU(5) or larger in bulk allows for gauge coupling unification at string scale

24. Title of talk23 Mini-Landscape search hep-th/0611095 Lebedev, Nilles, SR, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter

25. Title of talk24 Buchmuller, Hamaguchi, Lebedev & Ratz 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 Search for MSSM Spectra in heterotic orbifolds

26. Title of talk25 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

27. Title of talk26 Mini-Landscape search LNRRRVW

28. Title of talk27 Mini-Landscape search LNRRRVW 93 MSSM-like models or probability ~ 1/300 “Fertile patch” in heterotic landscape !!

29. Title of talk28 Road to the MSSM w/ R-parity LNRRRVW 0708.2691 [hep-th] 1. Check R parity 2. Check for D = 0 directions 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.

30. Title of talk29 R parity Forbid Dim 2 & 3 operators Family Reflection symmetry or Matter parity

31. Title of talk30 Generalized matter parity Z 2 Identify “suitable” B-L  standard for SM particles  vector-like on exotics  maximal no. SM singlets w/ Allow right-handed neutrino masses

32. Title of talk31 Results

33. Title of talk32 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.

34. Title of talk33 OOrbifold GUT - SU(6) LLocal GUT - SO(10) x SO(4)

35. Title of talk34 Spectrum

36. Title of talk35  term  ~ M Z Yukawa couplings Not realistic - YET

37. Title of talk36 Neutrino masses via See-Saw YES !! Dimension 5 operators – suppressed ~ BUT generated again when integrating out  s tates - problem ??

38. Title of talk37 Proton decay IF families at local GUT fixed points Dimension 6 ops. fixed by 1/ M C 2 Expect M C < M G Dimension 5 ops. unsuppressed - Unless find symmetry R-parity forbids Dimension 3 & 4 B & L violation

39. Title of talk38 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 MSSM Orbifold & Local GUT