SUSY Breaking in Local String Models

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SUSY Breaking in Local String Models
F. Quevedo, Cambridge/CERN. String
Phenomenology, Warsaw, June 2009.

• J.P. Conlon, A. Maharana, FQ
  arXiv0810.5660 hep-th
• R. Blumenhagen, J.P. Conlon, S. Krippendorf,
  S.Moster, FQ arXiv0906.xxxx hep-th
• See also S. de Alwis talk here

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Phenomenology
String Theory
String Phenomenology
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String Model Building

• Global Models (e.g. Heterotic)
• Local Brane Models (e.g. IIB)

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Bottom-up Approach
Aldazabal,Ibanez, FQ, Uranga 2000
Global (bulk) Issues Local (brane) Issues

• 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

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GLOBAL ISSUES
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LARGE Volume Scenario
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MODULI STABILISATION
4-cycle size t (Kahler moduli)
3-cycle size U (Complex structure moduli)
String Dilaton S
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Exponentially Large Volumes
BBCQ, CQS (2005)

• Perturbative (alpha) corrections to K

Example
Fluxes
Exponentially large volume, broken SUSY, AdS
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De Sitter? anti D3 or D,F uplifing
Model dependent e.g.
(Or W W0 f1f2e-aT2 )
LARGE volume de Sitter!
S. Krippendorf, FQ 2009
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General Conditions for LARGE Volume
Cicoli, Conlon, FQ

• h12 gt h11 gt 1
• At least one blow-up mode (point-like
  singularity)
• Blow-up mode fixed by non-perturbative effects,
  volume by alpha corrections

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e.g. Swiss Cheese Calabi-Yaus
e.g.
Blumenhagen, et al., Grimm et al., Kreuzer et al.
08
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Relevant Scales

• String scale MsMP/V 1/2
• Kaluza-Klein scale MKKMP/V 2/3
• Gravitino mass m3/2W0 MP/V

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Moduli Masses

• Dilaton Complex structure Mm3/2W0MP/V
• Small Kahler moduli M(lnV)m3/2
• Volume modulus MW0MP/V3/2 ltlt m3/2

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Original Scenarios

• MString MGUT 1016 GeV (V104-5)
• W010-11ltlt1 (or W01 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 (V1014)
• W01 (no hierarchy problem)
• m3/21 TeV
• QCD axion scale
• Neutrino masses LLHH
• Cosmological moduli problem, unification?
• MString 1 TeV (V1030)
• W01

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LOCAL ISSUES
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LARGE Volume Implies

• Standard Model is localised !
• ( SM D7 cannot wrap the exponentially large
  cycle
• since g21/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
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Universe D3 Brane or D7 Brane
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e.g. Standard Model at (Fractional) D3/D7 Branes
at Singularities
Collapsing single 4-cycle del Pezzo surfaces
dPn, n0,1, ,8 (P2 blown-up at n arbitrary
points c1gt0, b2n1, 2n-8 parameters, ngt3) More
general singularities, e.g. Ypq, Labc
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e.g. Realistic dP1 Models
LR Symmetric Model
Standard Model
Hierarchy in 3 generation masses!
Also Pati-Salam, etc.
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GLOBAL/LOCAL MIXING
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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 ltFgt0, so Wnp0,
(singularity)? Or ltF2gt
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Effective Field Theory I
Geometric Regime
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Effective Field Theory II
Around the Singularity (Blow-up Regime)
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SUSY BREAKING
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SM Cycle does not break SUSY!
Fayet-Iliopoulos ?0
Sequestered moduli/gravity mediated SUSY
Breaking
No-scale (vanishing soft terms)
Suppressed !
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Gravity/Moduli Mediated Soft-terms
Soft terms ltltlt M3/2 !!!
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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)
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New Scenarios

• Scalars 1/V3/2, others 1/V2
• All a/V3/2
• All 1/V2
• Loop corrections b/V5/3
• Mstring1013-1015 GeV
• Gauge mediation? (FX/xgtmltltM3/2?) but with heavy
  gravitino!

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General Properties

• Uplifting to de Sitter important
• Gravitino very heavy M3/2gt108 GeV !!
• Generically no CMP!!!! (MvolumegtMsoft)
• Minimal volume V106-7 .
• TeV soft terms and Mstring1015 GeV
  Unification scale MX Mstring V1/61016 GeV !
• Right scale for inflation!
• No CMP !!!

De Alwis 2006
Conlons talk
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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,)