Moduli Stabilization:Moduli Stabilization:

A Revolution in String A Revolution in String Phenomenology / Cosmology ? Phenomenology / Cosmology ?

F. Quevedo SUSY 2005

The ProblemThe Problem

String/M-Theory unique but has many solutions String/M-Theory unique but has many solutions or vacua.or vacua.

Some solutions resemble the Standard Model Some solutions resemble the Standard Model and MSSM.and MSSM.

Degeneracy : Discrete + Continuous (SUSY) .Degeneracy : Discrete + Continuous (SUSY) .

Outstanding Problems:Outstanding Problems: SUSY breaking + Vacuum degeneracy.SUSY breaking + Vacuum degeneracy.

HistoryHistory

t<1986 Calabi-Yau String Compactifications: Many free t<1986 Calabi-Yau String Compactifications: Many free

moduli (size and shape of extra dimensions)moduli (size and shape of extra dimensions)

1986<t<1991 Gaugino condensation and T-1986<t<1991 Gaugino condensation and T-duality duality

1991<t<2002 More moduli! (D-brane positions)1991<t<2002 More moduli! (D-brane positions)

t>2002 GKP/ KKLT : Fluxes fix modulit>2002 GKP/ KKLT : Fluxes fix moduli

Dilaton S, Kähler TComplex structure U

Fix S and one T

CHSWCHSW

DIN, DRSW, K, FILQ, FMTVDIN, DRSW, K, FILQ, FMTV

……GKP, KKLT, …GKP, KKLT, …

KKLT ScenarioKKLT Scenario

Type IIB String on Calabi-Yau orientifoldType IIB String on Calabi-Yau orientifold

Turn on FluxesTurn on Fluxes ∫∫aa FF33 = n = n aa ∫ ∫bb HH33 = m = m bb

SuperpotentialSuperpotential W =W = ∫ ∫ GG33 ΛΛ ΩΩ, G, G3 3 = = FF3 3 –iS–iS HH33

Scalar Potential:Scalar Potential: V= e V= eKK |D |DaaW|W|22 MinimumMinimum D DaaW = 0 W = 0 Fixes UFixes Uaa and S and S T moduli unfixed: T moduli unfixed: No-Scale modelsNo-Scale models

Size of cycle a = USize of cycle a = Uaa

GKPGKP

To fix KTo fix Kähler moduli: Non-perturbative D7 effectsähler moduli: Non-perturbative D7 effects

FluxesFluxes Non-perturbativeNon-perturbative

VolumeVolume

SUSY AdS minimumSUSY AdS minimum

(W(W00 << 1) << 1)

Lifting to de Sitter (add anti D3 branes, D-terms, etc.)Lifting to de Sitter (add anti D3 branes, D-terms, etc.)

SUSY breaking termSUSY breaking term

KKLT, BKQ, SSKKLT, BKQ, SS

VV

axionaxion volumevolume

The LandscapeThe Landscape

Huge number of discrete Huge number of discrete vacua >10vacua >10500500

StatisticsStatistics

Randall-Sundrum Randall-Sundrum warping from strings!warping from strings!

Non SUSY de SitterNon SUSY de Sitter

Dark energy?Dark energy?

`SM’ on D3/D7branes`SM’ on D3/D7branes

Soft SUSY breaking?Soft SUSY breaking?

Inflation?Inflation?

AD, DD, DDF, GKTT,CQ,BGHLWAD, DD, DDF, GKTT,CQ,BGHLW

GKPGKP

BPBP

CG-MQUCG-MQU

Realistic ModelsRealistic ModelsCG-MQU, CSUCG-MQU, CSU

Exponentially Large VolumesExponentially Large Volumes

At least two KAt least two Kähler moduli (hähler moduli (h2121>h>h1111>1)>1)

Perturbative corrections to KPerturbative corrections to K

Example :Example :

Exponentially large !Exponentially large !

BBCQ, CQSBBCQ, CQS

Non SUSY AdSNon SUSY AdS

WW00~1-10~1-10

String scale: MsString scale: Ms22=Mp=Mp22//VV

KKLT AdSKKLT AdS

Non SUSY AdSNon SUSY AdS

WW00~10~10-10-10

WW00<10<10-11-11

Both minima Both minima mergemerge

Soft SUSY BreakingSoft SUSY Breaking

From KKLT not explicit model but interesting general From KKLT not explicit model but interesting general behaviour (D/F term breaking, AMSB, …)behaviour (D/F term breaking, AMSB, …)

From lifting of large volume modelsFrom lifting of large volume models

MsMs~10~101313 GeV Gaugino masses ~ 10 GeV Gaugino masses ~ 1022 GeV, scalars m ~ GeV, scalars m ~ 101077 GeV GeV

Ms=MMs=MGUTGUT viable if warping, viable if warping,

Ms=Tev `viable’ if SM anti D-brane (but 5Ms=Tev `viable’ if SM anti D-brane (but 5thth force and cmp?) force and cmp?)

CFNOP,CJOCFNOP,CJO

CQSCQS

Matter on D3Matter on D3

INFLATION INFLATION

Racetrack InflationRacetrack Inflation

Topological eternal inflation !Topological eternal inflation !

Slow roll if 1/1000 fine tuning, Slow roll if 1/1000 fine tuning,

NN~60, ~60, δδHH~10~10-5 -5 for Ms~10for Ms~1015 15 GeVGeV

nnss ~ 0.95~ 0.95

B-PBCEG-RKLQB-PBCEG-RKLQ

D3 BraneD3 Brane

φφ

φφ inflaton field inflaton field

Brane- Antibrane inflationBrane- Antibrane inflation BMNRQZ, DSSBMNRQZ, DSS

KKLMMT, HKP, KTW, KKLMMT, HKP, KTW, FT, BCSQFT, BCSQ

Slow-roll (large field) inflation possible.Slow-roll (large field) inflation possible.

Need 1/1000 fine tuning of parameters to Need 1/1000 fine tuning of parameters to

get 60-efoldings (get 60-efoldings (ηη-problem)-problem)

NN~60, ~60, δδHH~10~10-5-5 for for

Ms~ 10Ms~ 101515 GeV GeV

nnss~1.05~1.05 BCSQBCSQ

VV

YYtachyontachyon

Tachyon complex topological defects Tachyon complex topological defects D (p-2) branes cosmic strings !D (p-2) branes cosmic strings !

End of inflation: Open string tachyonEnd of inflation: Open string tachyonBMNQRZBMNQRZ

ST, JST, CMPST, JST, CMP

S, BMNQRZS, BMNQRZ

Warped tachyonic inflationWarped tachyonic inflation

A,B depend on warping (fluxes) and E&M fields on non-A,B depend on warping (fluxes) and E&M fields on non-BPS brane. If A,BBPS brane. If A,B~1 no slow-roll~1 no slow-roll

AB large slow-rollAB large slow-roll

No fine-tuning! But need large fluxesNo fine-tuning! But need large fluxes

R, CQSR, CQS

INITIAL CONDITIONSINITIAL CONDITIONS

Sen’s open string Sen’s open string completeness completeness conjectureconjecture

t -tt -t

Pre big-bang ! ?Pre big-bang ! ?

Inflation and compactification or big-crunch/bangInflation and compactification or big-crunch/bang

and decompactification ! ?and decompactification ! ?

CONCLUSIONSCONCLUSIONS

Exciting timesExciting timesRS warping from CS sector, ADD large extra RS warping from CS sector, ADD large extra dimensions from Kdimensions from Kähler moduli sector.ähler moduli sector.Soft terms calculable for first time rich Soft terms calculable for first time rich phenomenologyphenomenologyExtensions to other string theoriesExtensions to other string theoriesConcrete models of inflationConcrete models of inflationSimple principles, complicated solutions, but SM Simple principles, complicated solutions, but SM is also ugly!is also ugly!Many open questionsMany open questions(A fully realistic model?)(A fully realistic model?)