Title of talk1 A Fertile Patch in the Heterotic Landscape Stuart Raby String Phenomenology CERN August 11, 2008

Title of talk2 Kobayashi, Raby, Zhang hep-ph/ , hep-ph/ Buchmuller, Hamaguchi, Lebedev & Ratz hep-ph/ , hep-ph/ Lebedev, Nilles, Raby, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter hep-th/ , hep-th/ , [hep-th] Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/ Dundee, Raby & Wingerter arXiv: [hep-th]

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

Title of talk4 String Model Building  Orbifold GUTs  Local GUTs  3 =  “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 …

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

Title of talk7  Perform focused search “Mini-Landscape” LNR 3 VW (see Wingerter talk)  Use both Local & Orbifold GUTs  Find ~ 200 MSSM-like models Consider properties of one “Benchmark” model in this talk See what MSSM-like means !

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. !

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

Title of talk10 Gauge lattice Embed twist in gauge lattice via shift Wilson lines

Title of talk11 Local SO(10) GUT Require massless SO(10) spinors at T 1 fixed points Mass operator

Title of talk12 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

Title of talk13 Consider massless Untwisted sector P 2 = 2 GSO projection Orbifold GUTs gaugeU3U3

Title of talk14 Gauge & U 3

Title of talk15 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

Title of talk16 2 (16) on SO(10) brane

Title of talk17 Third family & Higgs in BULK

Title of talk18 Discrete non-Abelian Family symmetry

Title of talk19 S 1 /Z

Title of talk20 D 4 family symmetry doubletsinglets geometryspace group sel. rule

Title of talk21 Fermion mass hierarchy

Title of talk22 Discrete Family Symmetries Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/ See also: D 4 phenomenology Ko, Kobayashi, Park & Raby arXiv:

Title of talk23 Benchmark model

Title of talk24 Exact R-parity !! U(1) B-L broken to Z 2 matter parity Forbids R-parity violating operators

Title of talk25  term  = 0 in flat space SUSY limit Yukawa couplings Neutrino masses via See-Saw Not realistic - yet

Title of talk26 Gauge coupling unification

Title of talk27 2 loop and weak scale corr’s KK modes exotics RG equations

Title of talk28 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

Title of talk29 Gauge coupling unification

Title of talk30 Proton Decay observable ?

Title of talk31 10D string coupling Dundee & Raby following Hebecker & Trapletti Weak Coupling !!

Title of talk32 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 ?

Title of talk33 Satisfies Gravity anomaly constraint Complete spectrum of 6D SU(6) orbifold GUT

Title of talk34 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/ 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

Title of talk35 Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa

Title of talk36 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 smooth K 3 xT 2 construction ??