1. Road to the MSSM thru M theory ? Stuart Raby University of Michigan Ann Arbor May 5, 2007

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

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

4. Cartan-Weyl

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

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

7. Title of talk7 Gauge coupling unification

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

9. Title of talk9 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino massesneutrino masses

10. Title of talk10 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino masses SO(10) SUSY GUT w/ L.E. SUSY

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

12. 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

13. Title of talk13 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  The road from M theory

14. Title of talk14 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

15. Title of talk15 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. !

16. Title of talk16 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

17. Title of talk17 Massless Untwisted sector P 2 = 2 GSO Gauge lattice

18. Title of talk18 E(6) x SU(3) Gauge & U 3

19. Title of talk19 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 )

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

21. Title of talk21  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

22. S 1 /Z 2 16 1 16 2

23. D 4 family symmetry doubletsinglet geometryspace group sel. rule

24. Title of talk24 Fermion mass hierarchy

25. Title of talk25 Mini-Landscape search hep-th/0611095 Lebedev, Nilles, SR, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter

26. Title of talk26 Buchmuller, Hamaguchi, Lebedev & Ratz Z 6 -II orbifold Looked for and found SM gauge group in 4D with 3 families and vector-like exotics Search for MSSM Spectra in heterotic orbifolds

27. Title of talk27 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

28. Title of talk28 Mini-Landscape search LNRRRVW

29. Title of talk29 Mini-Landscape search LNRRRVW 93 MSSM-like models or probability ~ 1/300 ‘Fertile’ patch in heterotic landscape !!

30. Title of talk30 Low Energy Supersymmetry from the Heterotic Landscape hep-th/0611203 Lebedev, Nilles, SR, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter

31. Title of talk31 Low Energy SUSY Breaking LNRRRVW Step 8 : 77 models

32. Title of talk32 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.

33. Title of talk33 Gluino condensate Assume stabilize S in Kahler potential & take

34. Title of talk34 Number of models vs. scale of gaugino condensation.

35. Title of talk35 LNRRRVW - in progress 1. Check for D = F = 0 directions 2. Check all exotics get mass 3. Check fermion masses 4. Check R parity conservation 5. Check neutrino masses ( 4 & 5 related ) 3( B – L) = 0 mod 2 “Family reflection symmetry” SUSY breaking and lifting flat directions ??

36. Title of talk36 The road from M theory 11 dim. Supergravity on R 3,1 x X 7 X 7 has G 2 holonomy Non-Abelian gauge fields on singularities with co-dimension 4 eg. X 7 = K 3 x T 3 with singular points in K 3

37. Title of talk37 E 8 x E 8 heterotic limit Horava - Witten 11 dim. Supergravity on R 3,1 x X 6 x S 1 /Z 2 X 6 has SU 3 holonomy Non-Abelian gauge fields on two 10 dim end-of-the-world branes

38. Title of talk38 E 8 x E 8 heterotic limit Compactify X 6 eg. X 6 = (T 2 ) 2 / Z 3 x T 2 & add Wilson line W 3 K 3 fixed points ? E(6) in 6 dim.

39. Title of talk39 CY 3 w/ K 3 fibration in type II dual to K 3 x T 2 = T 4 / Z N x T 2 in heterotic Kachru & Vafa hep-th/9505105 Vafa & Witten hep-th/9507050 Aldazabal, Font, Ibanez & Quevedo hep-th/9510093 Candelas & Font hep-th/9603170 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 use F theory

40. Title of talk40 Barshefsky, Intriligator, Kachru, Morrison, Sadov & Vafa

41. Title of talk41 F theory on heterotic/type II duality Compactified on K 3 x T 2 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 E 8 w/ 10 instantons  E 6 + 4 (27 + c.c.) E 8 w/ 14 instantons  SO 10 + 6 (16 + c.c.) + 8 (10 + c.c.) K 3 + instantons = T 4 / Z 3 + Wilson line !!!

42. Title of talk42 On the Duality between perturbative heterotic orbifolds and M theory on T 4 /Z N [ orbifold limit of K 3 ] X 6 = T 4 / Z N x T 2 w/N = 2, 3, 4, 6 dual to X 7 = T 4 / Z N x T 2 x S 1 / Z 2 Kaplunovsky, Sonnenschein, Theisen & Yankielowicz hep-th/9912144 Faux, Lust & Ovrut hep-th/0010087

43. Title of talk43 On the Duality between heterotic on T 3 x R 6,1 and M theory on K 3 x R 6,1 Is there a useful duality between E(8)xE(8) heterotic on T 4 x T 2 x R 3,1 orbifolded and M theory on K 3 x S 1 x [ S 2 x R 3,1 ] ?? Acharya & Gukov hep-th/0409191

44. Title of talk44 String threshold corrections & Gauge coupling unification Ibanez & Lust hep-th/9202046 Calculate moduli dependence of string threshold corrections Show : Only certain orbifolds with T 1 >> T 2, T 3 are consistent with M GUT < M string Z 6 -II, Z 8 & Z N x Z M !!

45. Title of talk45 Conclusions We find MSSM in ‘fertile patch’ of E(8)xE(8) heterotic string compactified on orbifold [(T 4 / Z 3 ) x T 2 ]/Z 2 IS there an M theory dual ?? use to understand moduli stabilization and SUSY breaking a la Acharya et al. Important to test string theory