SUSY Breaking in Local String Models

F. Quevedo, Cambridge/CERN. String Phenomenology, Warsaw, June 2009.

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

Phenomenology String Theory String Phenomenology

String Model Building:



Global Models (e.g. Heterotic)



Local Brane Models (e.g. IIB)

Bottom-up Approach

Aldazabal,Ibanez, FQ, Uranga 2000

Global (bulk) Issues Local (brane) Issues

• • • • • •

Moduli Stabilisation Cosmological constant SUSY Breaking Scales (unification, axions,…) Inflation, Reheating Cosmological moduli problem

• • • • • •

Gauge group Chiral spectrum Yukawa couplings Gauge couplings Proton stability Flavour symmetries

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

BBCQ, CQS (2005)

Perturbative (alpha’) corrections to K Example : Fluxes Exponentially large volume, broken SUSY, AdS

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

S. Krippendorf, FQ 2009

General Conditions for LARGE Volume

Cicoli, Conlon, FQ •

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

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 ~ 10 16 GeV (V~10 4-5 ) W 0 ~10 -11 <<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.

~ 10 12 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~10 -15 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

Blumenhagen talk

Local F-Theory

Heckman, Tatar, … talks

Universe D3 Brane 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

LR Symmetric Model Standard Model Also: Pati-Salam, etc.

Hierarchy in 3 generation masses!

GLOBAL/LOCAL MIXING

Local/Global Mixing

• •

Standard Model in small cycle SM cycle NOT fixed by non-perturbative effects:

•

SM chiral implies:

W np =

Blumenhagen et al.2007

MSSM: < Φ>=0, so W np =0, (singularity)? Or <| Φ| 2 >=

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 Independent of SUSY breaking fields

( )

All soft terms of order (loop factor)/V 3/2 or 1/V 2 (e.g. anomaly mediation and/or Dilaton F-term)

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 ~10 13 -10 15 GeV Gauge mediation? (F X /x>m<

General Properties

• • • •

Uplifting to de Sitter important

De Alwis 2006

Gravitino very heavy M 3/2 >10 8 GeV !!

Generically no CMP!!!! (M volume >M soft ) Minimal volume V~10 6-7 .

TeV soft terms and M string ~10 15 Unification scale M X ~ M string GeV V 1/6 ~10 16 GeV !

Conlon’s talk

Right scale for inflation!

No CMP !!!

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,…)