SUSY Breaking in Local String Models J.P. Conlon, A. Maharana, FQ arXiv: [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.

Phenomenology String Theory String Phenomenology

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

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

GLOBAL ISSUES

LARGE Volume Scenario

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

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

De Sitter?: anti D3 or D,F uplifing (Or W~ W 0 + φ 1 φ 2 e -aT2 ) LARGE volume de Sitter! S. Krippendorf, FQ 2009 Model dependent e.g.:

General Conditions for LARGE Volume h 12 > h 11 > 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

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

Relevant Scales String scale Ms=M P /V 1/2 Kaluza-Klein scale M KK =M P /V 2/3 Gravitino mass m 3/2 =W 0 M P /V

Moduli Masses Dilaton + Complex structure M~m 3/2 =W 0 M P /V ‘Small’ Kahler moduli M~(lnV)m 3/2 Volume modulus M~W 0 M P /V 3/2 << m 3/2

Original Scenarios M String = M GUT ~ GeV (V~ ) W 0 ~ <<1 (or W 0 ~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! M String = M int. ~ GeV (V~10 14 ) W 0 ~1 (no hierarchy problem) m 3/2 ~1 TeV QCD axion scale Neutrino masses LLHH Cosmological moduli problem, unification? M String = 1 TeV (V~10 30 ) W 0 ~1 Most exciting, but 5th Force (volume modulus m~ eV)??

LOCAL ISSUES

LARGE Volume Implies Standard Model is localised ! ( SM D7 cannot wrap the exponentially large cycle since g 2 =1/V 2/3 )  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

Universe D3 Brane or or D7 Brane

e.g. Standard Model at (Fractional) D3/D7 Branes at Singularities Collapsing single 4-cycle: del Pezzo surfaces dP n, n=0,1, …,8 (P 2 blown-up at n arbitrary points c 1 >0, b 2 =n+1, 2n-8 parameters, n>3) More general singularities, e.g. Y pq, L abc

e.g. Realistic dP 1 Models Standard Model LR Symmetric Model Hierarchy in 3 generation masses! Also: Pati-Salam, etc.

GLOBAL/LOCAL MIXING

Local/Global Mixing Standard Model in small cycle SM cycle NOT fixed by non-perturbative effects: SM chiral implies: W np = MSSM: =0, so W np =0, (singularity)? Or = Blumenhagen et al.2007

Effective Field Theory I Geometric Regime

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

SUSY BREAKING

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

Gravity/Moduli Mediated Soft-terms Soft terms <<< M 3/2 !!!

Local Yukawas and SUSY Breaking () All soft terms of order (loop factor)/V 3/2 or 1/V 2 (e.g. anomaly mediation and/or Dilaton F-term) Independent of SUSY breaking fields

New Scenarios Scalars 1/V 3/2, others 1/V 2 All a/V 3/2 All 1/V 2 Loop corrections ~ b/V 5/3 M string ~ GeV Gauge mediation? (F X /x>m<<M 3/2 ?) but with heavy gravitino!

General Properties Uplifting to de Sitter important Gravitino very heavy M 3/2 >10 8 GeV !! Generically no CMP!!!! (M volume >M soft ) Minimal volume V~ TeV soft terms and M string ~10 15 GeV Unification scale M X ~ M string V 1/6 ~10 16 GeV ! Right scale for inflation! No CMP !!! Conlon’s talk De Alwis 2006

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,…)