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SUSY Breaking in Local String Models

SUSY Breaking in Local String Models. J.P. Conlon, A. Maharana, FQ arXiv:0810.5660 [hep-th] ] R. Blumenhagen, J.P. Conlon, S. Krippendorf, S.Moster, FQ arXiv:0906.xxxx [hep-th] See also S. de Alwis talk here. F. Quevedo, Cambridge/CERN. String Phenomenology, Warsaw, June 2009.

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SUSY Breaking in Local String Models

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  1. SUSY Breaking in Local String Models J.P. Conlon, A. Maharana, FQarXiv:0810.5660 [hep-th]] R. Blumenhagen, J.P. Conlon, S. Krippendorf, S.Moster, FQ arXiv:0906.xxxx [hep-th] See also S. de Alwis talk here F. Quevedo, Cambridge/CERN. String Phenomenology, Warsaw, June 2009.

  2. Phenomenology String Theory String Phenomenology

  3. String Model Building: • Global Models (e.g. Heterotic) • Local Brane Models (e.g. IIB)

  4. Gauge group Chiral spectrum Yukawa couplings Gauge couplings Proton stability Flavour symmetries Moduli Stabilisation Cosmological constant SUSY Breaking Scales (unification, axions,…) Inflation, Reheating Cosmological moduli problem Bottom-up Approach Aldazabal,Ibanez, FQ, Uranga 2000 Global (bulk) Issues Local (brane) Issues

  5. GLOBAL ISSUES

  6. LARGE Volume Scenario

  7. MODULI STABILISATION 4-cycle size: τ (Kahler moduli) 3-cycle size: U (Complex structure moduli) + String Dilaton: S

  8. Exponentially Large Volumes BBCQ, CQS (2005) • Perturbative (alpha’) corrections to K Example : Fluxes Exponentiallylarge volume, broken SUSY, AdS

  9. De Sitter?: anti D3 or D,F uplifing Model dependent e.g.: (Or W~ W0 + φ1φ2e-aT2 ) LARGE volume de Sitter! S. Krippendorf, FQ 2009

  10. General Conditions for LARGE Volume • h12 > h11 > 1 • At least one blow-up mode (point-like singularity) • Blow-up mode fixed by non-perturbative effects, volume by alpha’ corrections Cicoli, Conlon, FQ

  11. e.g. Swiss Cheese Calabi-Yau’s e.g. Blumenhagen, et al., Grimm et al., Kreuzer et al. 08

  12. Relevant Scales • String scale Ms=MP/V 1/2 • Kaluza-Klein scale MKK=MP/V 2/3 • Gravitino mass m3/2=W0 MP/V

  13. Moduli Masses • Dilaton + Complex structure M~m3/2=W0MP/V • ‘Small’ Kahler moduli M~(lnV)m3/2 • Volume modulus M~W0MP/V3/2 <<m3/2

  14. Original Scenarios • MString = MGUT~ 1016 GeV (V~104-5) • W0~10-11<<1 (or W0~1 plus warping) • Fits with coupling unification • Natural scale of most (all?) string inflation models. • Axi-volume quintessence scale (w=-0.999….) • Cosmological moduli problem! • MString = Mint.~ 1012 GeV (V~1014) • W0~1 (no hierarchy problem) • m3/2~1 TeV • QCD axion scale • Neutrino masses LLHH • Cosmological moduli problem, unification? • MString = 1 TeV(V~1030) • W0~1 • Most exciting, but 5th Force (volume modulus m~10-15 eV)??

  15. LOCAL ISSUES

  16. LARGE Volume Implies Standard Model is localised ! ( SM D7 cannot wrap the exponentially large cycle since g2=1/V2/3 ) • Fractional D3/D7 Brane at a singularity (collapsed cycle) • Magnetised D7 - Brane wrapping a ‘small’ four-cycle • Local F-Theory Blumenhagen talk Heckman, Tatar, … talks

  17. Universe D3 Brane or D7 Brane

  18. e.g. Standard Model at (Fractional) D3/D7 Branes at Singularities Collapsing single 4-cycle: del Pezzo surfaces dPn, n=0,1, …,8 (P2 blown-up at n arbitrary points c1>0, b2=n+1, 2n-8 parameters, n>3) More general singularities, e.g. Ypq, Labc

  19. e.g. Realistic dP1 Models LR Symmetric Model Standard Model Hierarchy in 3 generation masses! Also: Pati-Salam, etc.

  20. GLOBAL/LOCAL MIXING

  21. Local/Global Mixing • Standard Model in small cycle • SM cycle NOT fixed by non-perturbative effects: • SM chiral implies:Wnp= Blumenhagen et al.2007 MSSM: <Φ>=0, so Wnp=0, (singularity)? Or <|Φ|2>=

  22. Effective Field Theory I Geometric Regime

  23. Effective Field Theory II Around the Singularity (Blow-up Regime)

  24. SUSY BREAKING

  25. SM Cycle does not break SUSY! ‘Fayet-Iliopoulos’ 0 ‘Sequestered moduli/gravity mediated SUSY Breaking’ No-scale (vanishing soft terms) Suppressed !

  26. Gravity/Moduli Mediated Soft-terms Soft terms <<< M3/2 !!!

  27. Local Yukawas and SUSY Breaking ( ) Independent of SUSY breaking fields All soft terms of order (loop factor)/V3/2 or 1/V2 (e.g. anomaly mediation and/or Dilaton F-term)

  28. New Scenarios • Scalars 1/V3/2, others 1/V2 • All a/V3/2 • All 1/V2 • Loop corrections ~ b/V5/3 • Mstring~1013-1015 GeV • Gauge mediation? (FX/x>m<<M3/2?) but with heavy gravitino!

  29. General Properties • Uplifting to de Sitter important • Gravitino very heavy M3/2>108 GeV !! • Generically no CMP!!!! (Mvolume>Msoft) • Minimal volume V~106-7 . TeV soft terms and Mstring~1015 GeV Unification scale MX~ Mstring V1/6~1016 GeV ! Right scale for inflation! No CMP !!! De Alwis 2006 Conlon’s talk

  30. Conclusions • Continuous progress in this `Decade of Applied String Theory’ • Bottom-up (Local Model Building) fits with Large Volume • Realistic models at singularities: powerful quiver/dimer constructions • New SUSY breaking scenarios with TeV soft terms and GUT scale unification • Alleviate tension between low energy SUSY and cosmology • Generically no CMP!!! • Open challenges (compact CY, detailed susy breaking, EFT in F-theory models,…)

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