Title of talk1 On the Heterotic Road to the MSSM Stuart Raby Eotvos-Cornell 2007 Budapest, Hungary June 29, 2007

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

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

4 spinor repsn. of SO( 10 ) Charge quantization

Title of talk5 Phenomenology  charge quantization  gauge coupling unificationgauge coupling unification  Yukawa unification  neutrino masses

Title of talk6 Phenomenology  charge quantization  gauge coupling unification  Yukawa unificationYukawa unification  neutrino masses

Title of talk7 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino massesneutrino masses

Title of talk8 Phenomenology  charge quantization  gauge coupling unification  Yukawa unification  neutrino masses SO(10) SUSY GUT w/ L.E. SUSY

Title of talk9 4 D GUT problems GUT symmetry breaking Higgs doublet – triplet splitting Solution ? Orbifold GUTs

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

Title of talk11 Outline  Orbifold GUTs / String Orbifolds Kobayashi, SR, Zhang hep-ph/ , hep-ph/  Mini-Landscape I: search for MSSM Lebedev et al hep-th/ , hep-th/ L-II : Approaching the MSSM Lebedev et al - in preparation

Title of talk12 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

Title of talk13 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. !

Title of talk14 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

Title of talk15 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 )

Title of talk16 T 1 twisted sector 2 Light fam’s Local GUT SO(10)

Title of talk17 T 1 twisted sector Vector-like exotics Can get large mass & decouple !!

Title of talk18 T 1 twisted sector Vector-like exotics ASIDE: Some EXOTICA do not affect GUT predictions !!

Title of talk19 S.R. & Wingerter [hep-ph] baryon s mesons EXOTICA > 200 GeV

Title of talk20 exothermi c ~ sec ~ sec Only problem - searches for heavy hydrogen ?? Mesons  Baryons Easily produced at LHC

Title of talk21 Mini-Landscape search hep-th/ Lebedev, Nilles, SR, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter Search for MSSM Spectra in heterotic orbifolds

Title of talk22 Follow lead of Buchmuller, Hamaguchi, Lebedev & Ratz using same Z 6 -II orbifold hep-ph/ , hep-ph/ Looked for and found SM gauge group in 4D with 3 families and vector-like exotics

Title of talk23 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

Title of talk24 Mini-Landscape search LNRRRVW

Title of talk25 Mini-Landscape search LNRRRVW 93 MSSM-like models or probability ~ 1/300 ‘Fertile’ patch in heterotic landscape !! w/ Arbitrary singlet VEVs

Title of talk26 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

Title of talk27 ML: 1170 ML: 127

Title of talk28 Sin 2  90% in SU(5) Only ~ 10% w/ Sin 2  1220 models

Title of talk29 ML-II : Approaching the MSSM LNRRRVW – in preparation 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.

Title of talk30 Generalized R parity Forbid Dim 2 & 3 operators Family Reflection symmetry or Matter parity

Title of talk31 Construct model w/ Generalized R parity Identify “suitable” B-L  standard for SM particles  vector-like on exotics  maximal no. SM singlets w/

Title of talk32 Results

Title of talk33 Results

Title of talk34 Consider One 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.

Title of talk35 OOrbifold GUT - SU(6) LLocal GUT - SO(10) x SO(4)

Title of talk36 Spectrum

Title of talk37  term  ~ M Z Yukawa couplings Not realistic - YET

Title of talk38 Neutrino masses via See-Saw YES !! Dimension 5 operators – suppressed ~

Title of talk39 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 theory !!! w/ Caveat MSSM Orbifold & Local GUT

Title of talk40