Moduli Stabilization A Revolution in String Phenomenology Cosmology

Moduli Stabilization: A Revolution in String Phenomenology / Cosmology ? F. Quevedo SUSY 2005

The Problem String/M-Theory unique but has many solutions or vacua. Some solutions resemble the Standard Model and MSSM. Degeneracy : Discrete + Continuous (SUSY). Outstanding Problems: SUSY breaking + Vacuum degeneracy.

History t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) Dilaton S, Kähler T Complex structure U CHSW 1986<t<1991 Gaugino condensation and Tduality DIN, DRSW, K, FILQ, FMTV Fix S and one T 1991<t<2002 More moduli! (D-brane positions) t>2002 GKP/ KKLT : Fluxes fix moduli …GKP, KKLT, …

KKLT Scenario Type IIB String on Calabi-Yau orientifold Turn on Fluxes ∫a F 3 = n a ∫ b H 3 = m b Superpotential W = ∫ G 3 Λ Ω, Scalar Potential: Size of cycle a = Ua G 3 = F 3 –i. S H 3 V= e. K |Da. W|2 Minimum Da. W = 0 Fixes Ua and S T moduli unfixed: No-Scale models GKP

To fix Kähler moduli: Non-perturbative D 7 effects Fluxes Volume SUSY Ad. S minimum (W 0 << 1) Non-perturbative

Lifting to de Sitter (add anti D 3 branes, D-terms, etc. ) KKLT, BKQ, SS SUSY breaking term V axion volume

The Landscape Huge number of discrete vacua >10500 Statistics AD, DDF, GKTT, CQ, BGHLW Randall-Sundrum warping GKP from strings! Non SUSY de Sitter Dark energy? BP `SM’ on D 3/D 7 branes CG-MQU Soft SUSY breaking? Inflation?

Realistic Models CG-MQU, CSU

Exponentially Large Volumes BBCQ, CQS At least two Kähler moduli (h 21>h 11>1) Perturbative corrections to K Example : Exponentially large !

Non SUSY Ad. S W 0~1 -10 String scale: Ms 2=Mp 2/V

KKLT Ad. S Non SUSY Ad. S Both minima merge W 0~10 -10 W 0<10 -11

Soft SUSY Breaking From KKLT not explicit model but interesting general behaviour (D/F term breaking, AMSB, …) CFNOP, CJO From lifting of large volume models CQS Matter on D 3 Ms~1013 Ge. V Gaugino masses ~ 102 Ge. V, scalars m ~ 107 Ge. V Ms=MGUT viable if warping, Ms=Tev `viable’ if SM anti D-brane (but 5 th force and cmp? )

INFLATION B-PBCEG-RKLQ Topological eternal inflation ! Racetrack Inflation Slow roll if 1/1000 fine tuning, N~60, δH~10 -5 for Ms~1015 Ge. V ns ~ 0. 95

Brane- Antibrane inflation BMNRQZ, DSS KKLMMT, HKP, KTW, FT, BCSQ φ inflaton field D 3 Brane φ

Slow-roll (large field) inflation possible. Need 1/1000 fine tuning of parameters to get 60 -efoldings (η-problem) N~60, δH~10 -5 for Ms~ 1015 Ge. V ns~1. 05 BCSQ

End of inflation: Open string tachyon BMNQRZ V Y Tachyon complex D (p-2) branes topological defects cosmic strings ! ST, JST, CMP tachyon S, BMNQRZ

R, CQS A, B depend on warping (fluxes) and E&M fields on non. BPS brane. If A, B~1 no slow-roll Warped tachyonic inflation AB large slow-roll No fine-tuning! But need large fluxes

INITIAL CONDITIONS Sen’s open string completeness conjecture t -t Pre big-bang ! ? Inflation and compactification or big-crunch/bang and decompactification ! ?

CONCLUSIONS Exciting times RS warping from CS sector, ADD large extra dimensions from Kähler moduli sector. Soft terms calculable for first time rich phenomenology Extensions to other string theories Concrete models of inflation Simple principles, complicated solutions, but SM is also ugly! Many open questions (A fully realistic model? )