Large Volume String Large Volume String CompactificationsCompactifications

hep-th/0505076, 0509012, 0605141, 0609180, hep-ph/0512081 and to appearhep-th/0505076, 0509012, 0605141, 0609180, hep-ph/0512081 and to appear

F. Quevedo, Cambridge. UKBSM Liverpool 2007(J. Conlon, K. Suruliz, D. Cremades, S. Abdussalam,B. Allanach, S. Kom, V.Balasubramanian, P. Berglund, …)

OUTLINEOUTLINE

Moduli Stabilisation and the String Moduli Stabilisation and the String LandscapeLandscapeExponentially Large VolumesExponentially Large VolumesSUSY Breaking SUSY Breaking (LHC Phenomenology)(LHC Phenomenology)

Cosmology Cosmology (Inflation, CMP,…)(Inflation, CMP,…)

ConclusionsConclusions

Moduli Stabilisation and Moduli Stabilisation and the String Landscapethe String Landscape

The ProblemThe Problem

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

Some solutions resemble the Standard Model Some solutions resemble the Standard Model and MSSM but moduli unrealistic.and MSSM but moduli unrealistic.

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

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

Dilaton S, Kähler TComplex structure UWilson lines W, Brane separation Y

KKLT ScenarioKKLT Scenario Type IIB String on Calabi-Yau Type IIB String on Calabi-Yau

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, SS,…KKLT, BKQ, SS,…

VV

axionaxion volumevolume

The LandscapeThe Landscape

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

StatisticsStatisticsRandall-Sundrum Randall-Sundrum warping from strings!warping from strings!Non SUSY de SitterNon SUSY de SitterDark energy?Dark energy?

AD, DD, AD, DD, GKTT,CQ,BGHLWGKTT,CQ,BGHLW

GKPGKP

BPBP

Exponentially Large VolumesExponentially Large Volumes

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

SUSY BreakingSUSY Breaking(LHC Signatures)(LHC Signatures)

The Standard Model in the CYThe Standard Model in the CY

4D effective Action4D effective Action

ΦΦ moduli, C matter, H Higgs moduli, C matter, H Higgs

New!New!

Chiral matter in CYChiral matter in CYConlon, Cremades, FQ Conlon, Cremades, FQ

Soft SUSY BreakingSoft SUSY Breaking

Large Volume (SM on D3 brane)Large Volume (SM on D3 brane)

MsMs~10~101313 GeV Gaugino masses ~ 10 GeV Gaugino masses ~ 1022 GeV, scalars m ~ GeV, scalars m ~ 101077 GeV GeVMs=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?)

CQS, AQSCQS, AQS

Matter on D3Matter on D3

Standard Model on D3 BraneStandard Model on D3 BraneTwo General ScenariosTwo General Scenarios

Intermediate Scale Split SUSYIntermediate Scale Split SUSY

Stringy mSUGRAStringy mSUGRA

SM on D3 brane, Ms=10SM on D3 brane, Ms=101212GevGev

SM on D3 brane, Ms=10SM on D3 brane, Ms=101717GevGev

Do not solve hierarchy problem(?)Do not solve hierarchy problem(?)

Standard Model on D7 BranesStandard Model on D7 Branes

Solve hierarchy problem Solve hierarchy problem MMstringstring = 10 = 101111 GeV!GeV!

WW00~1 (no fine tuning)~1 (no fine tuning)

Kahler potential for Kahler potential for chiralchiral matter computed matter computedConlon, Cremades, FQ Conlon, Cremades, FQ

Chiral Matter on D7 BranesChiral Matter on D7 BranesSoft SUSY Breaking termsSoft SUSY Breaking terms

• Universality!Universality!• No extra CP violation!No extra CP violation!• MMii = m = m3/23/2 / log (Mp/m / log (Mp/m3/23/2))• String scale 10String scale 101111 GeV GeV • Solves hierarchy problem!Solves hierarchy problem!

Conlon et al.Conlon et al.

Simplest caseSimplest case

More general caseMore general case

Stringy source of universalityStringy source of universality(approximate)(approximate)

CP ViolationCP Violation

Physical phases vanish !Physical phases vanish !

Also: Anomaly mediation suppressed !Also: Anomaly mediation suppressed !

From Strings to LHC dataFrom Strings to LHC data

Stabilise Moduli Stabilise Moduli SUSY broken with hierarchy SUSY broken with hierarchy ““Realistic” Observable sector Realistic” Observable sector Soft SUSY Breaking termsSoft SUSY Breaking terms@Ms @Ms RG-Running of Soft terms to TeV RG-Running of Soft terms to TeV (softsusy)(softsusy) Event Generators Event Generators (PYTHIA-Herwig)(PYTHIA-Herwig)

Detector Simulators Detector Simulators (PGS, GEANT)(PGS, GEANT)

Data AnalysisData Analysis (Root) (Root)

Estimate overall uncertaintyEstimate overall uncertainty

Allowed RegionsAllowed Regions

Renormalisation group runRenormalisation group run

Low energy spectrumLow energy spectrum

Some observablesSome observables

Sources ofSources of uncertaintyuncertainty

• Gaugino massesGaugino masses

• Spectrum Beyond MSSMSpectrum Beyond MSSM

Spectrum uncertaintySpectrum uncertainty

Comparison Comparison with with MSUGRAMSUGRA

Smoking gun?Smoking gun?

Gaugino massesGaugino masses

Scalar masses (focus)Scalar masses (focus)

Large volumeLarge volume

MSUGRAMSUGRA

Intermediate vsIntermediate vs GUT scale !GUT scale !

CosmologyCosmology

(Inflation, Cosmological moduli (Inflation, Cosmological moduli problem, etc.)problem, etc.)

InflationInflationNeed to compute scalar potential from String Need to compute scalar potential from String theory satisfying slow-roll conditions:theory satisfying slow-roll conditions:

Number of e-folds N>60

Density perturbations

Inflation and Moduli StabilisationInflation and Moduli Stabilisation

Brane-antibrane inflation (also DBI)Brane-antibrane inflation (also DBI)

Racetrack inflationRacetrack inflation

First explicit inflation realisations in string theoryFirst explicit inflation realisations in string theory

Fine tuning 1/1000 or large fluxes ?Fine tuning 1/1000 or large fluxes ?

KKähler Moduli Inflationähler Moduli Inflation

Calabi-Yau: h2121>>h1111>2

volume τn

V

Conlon-FQ Conlon-FQ

Bond-Kofman-ProkushkinBond-Kofman-Prokushkin

Small field inflationNo fine-tuning!!0.960<n<0.967

GUT scale Ms?, Loops?GUT scale Ms?, Loops?

Other Cosmological ImplicationsOther Cosmological ImplicationsCosmological moduli problemCosmological moduli problem

Observational implications of light volume Observational implications of light volume modulus?modulus?

U,S: trapped at their minimumU,S: trapped at their minimumT: except for volume, heavy ad decay fast ! (No T: except for volume, heavy ad decay fast ! (No

CMP nor gravitino overproduction)CMP nor gravitino overproduction)Volume: (mass MeV) CMP (thermal inflation?). Volume: (mass MeV) CMP (thermal inflation?).

Dark matter?Dark matter?

X-rays,Gamma rays, eX-rays,Gamma rays, e++-e-e- - (511 KeV?)(511 KeV?)

CONCLUSIONSCONCLUSIONS

Exciting times for string phenomenology!Exciting times for string phenomenology!Soft terms calculable for first time rich Soft terms calculable for first time rich phenomenologyphenomenologyIntermediate scale strings: hierarchy, QCD Intermediate scale strings: hierarchy, QCD axions, neutrino masses axions, neutrino masses (Conlon, Conlon+Cremades)(Conlon, Conlon+Cremades)

Concrete models of inflationConcrete models of inflationModel independent light modulusModel independent light modulusMany open questionsMany open questions(A fully realistic model?)(A fully realistic model?)

(String Vacuum Project (SVP)?)(String Vacuum Project (SVP)?)