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Moduli Stabilization and Large Volume Compactifications in String Theory

This paper explores the challenges of moduli stabilization within the framework of string theory, emphasizing the vast landscape of potential solutions or vacua. It discusses the KKLT scenario and its implications for stabilizing moduli while keeping the string theory viable. Focusing on exponentially large volumes, SUSY breaking phenomena, and implications for LHC phenomenology, it also tackles cosmological aspects like inflation and the cosmological moduli problem. The findings highlight an exciting evolution in string phenomenology with calculable soft terms and the potential for realistic models.

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Moduli Stabilization and Large Volume Compactifications in String Theory

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  1. Large Volume String Compactifications hep-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, …)

  2. OUTLINE • Moduli Stabilisation and the String Landscape • Exponentially Large Volumes • SUSY Breaking (LHC Phenomenology) • Cosmology (Inflation, CMP,…) • Conclusions

  3. Moduli Stabilisation and the String Landscape

  4. The Problem • String/M-Theory unique but has many solutions or vacua. Moduli: • Some solutions resemble the Standard Model and MSSM but moduli unrealistic. • Degeneracy : Discrete + Continuous (SUSY) . • Outstanding Problems: Dilaton S, Kähler T Complex structure U Wilson lines W, Brane separation Y SUSY breaking + Vacuum degeneracy.

  5. KKLT Scenario • Type IIB String on Calabi-Yau • Turn on Fluxes ∫aF3 = n a ∫bH3 = m b SuperpotentialW = ∫ G3ΛΩ, G3 = F3 –iSH3 Scalar Potential: V= eK |DaW|2 Minimum DaW = 0 Fixes Ua and S T moduli unfixed: No-Scale models Size of cycle a = Ua GKP

  6. To fix Kähler moduli: Non-perturbative D7 effects Non-perturbative Fluxes Volume SUSY AdS minimum (W0 << 1)

  7. Lifting to de Sitter (add anti D3 branes, D-terms, etc.) KKLT, BKQ, SS,… SUSY breaking term V axion volume

  8. The Landscape • Huge number of discrete vacua >10500 • Statistics • Randall-Sundrum warping from strings! • Non SUSY de Sitter • Dark energy? AD, DD, GKTT,CQ,BGHLW GKP BP

  9. Exponentially Large Volumes

  10. Exponentially Large Volumes BBCQ, CQS • At least two Kähler moduli (h21>h11>1) • Perturbative corrections to K Example : Exponentially large !

  11. Non SUSY AdS W0~1-10 String scale: Ms2=Mp2/V

  12. KKLT AdS Non SUSY AdS Both minima merge W0~10-10 W0<10-11

  13. SUSY Breaking (LHC Signatures)

  14. The Standard Model in the CY

  15. 4D effective Action Φ moduli, C matter, H Higgs New! Chiral matter in CY Conlon, Cremades, FQ

  16. Soft SUSY Breaking • Large Volume (SM on D3 brane) CQS, AQS Matter on D3 Ms~1013 GeV Gaugino masses ~ 102 GeV, scalars m ~107 GeV Ms=MGUT viable if warping, Ms=Tev `viable’ if SM anti D-brane (but 5th force and cmp?)

  17. Standard Model on D3 BraneTwo General Scenarios • Intermediate Scale Split SUSY • Stringy mSUGRA SM on D3 brane, Ms=1012Gev SM on D3 brane, Ms=1017Gev Do not solve hierarchy problem(?)

  18. Standard Model on D7 Branes • Solve hierarchy problem Mstring = 1011GeV! • W0~1 (no fine tuning) • Kahler potential for chiral matter computed Conlon, Cremades, FQ

  19. Chiral Matter on D7 Branes Soft SUSY Breaking terms Simplest case Conlon et al. • Universality! • No extra CP violation! • Mi = m3/2 / log (Mp/m3/2) • String scale 1011 GeV • Solves hierarchy problem! More general case

  20. Stringy source of universality(approximate) CP Violation Physical phases vanish ! Also: Anomaly mediation suppressed !

  21. From Strings to LHC data • Stabilise Moduli • SUSY broken with hierarchy • “Realistic” Observable sector • Soft SUSY Breaking terms@Ms • RG-Running of Soft terms to TeV (softsusy) • Event Generators (PYTHIA-Herwig) • Detector Simulators (PGS, GEANT) • Data Analysis (Root) • Estimate overall uncertainty

  22. Renormalisation group run Allowed Regions

  23. Low energy spectrum

  24. Some observables

  25. Sources ofuncertainty • Gaugino masses • Spectrum Beyond MSSM

  26. Spectrum uncertainty

  27. Comparison with MSUGRA

  28. Smoking gun? • Gaugino masses • Scalar masses (focus) Large volume MSUGRA Intermediate vs GUT scale !

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

  30. Inflation • Need to compute scalar potential from String theory satisfying slow-roll conditions: Number of e-folds N>60 Density perturbations

  31. Inflation and Moduli Stabilisation • Brane-antibrane inflation (also DBI) • Racetrack inflation First explicit inflation realisations in string theory Fine tuning 1/1000 or large fluxes ?

  32. Kähler Moduli Inflation Conlon-FQ Bond-Kofman-Prokushkin Calabi-Yau: h21>h11>2 Small field inflation No fine-tuning!! 0.960<n<0.967 V τn volume GUT scale Ms?, Loops?

  33. Other Cosmological Implications • Cosmological moduli problem • Observational implications of light volume modulus? U,S: trapped at their minimum T: except for volume, heavy ad decay fast ! (No CMP nor gravitino overproduction) Volume: (mass MeV) CMP (thermal inflation?). Dark matter? X-rays,Gamma rays, e+-e- (511 KeV?)

  34. CONCLUSIONS • Exciting times for string phenomenology! • Soft terms calculable for first time rich phenomenology • Intermediate scale strings: hierarchy, QCD axions, neutrino masses (Conlon, Conlon+Cremades) • Concrete models of inflation • Model independent light modulus • Many open questions (A fully realistic model?) (String Vacuum Project (SVP)?)

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