Meta-stable Supersymmetry Breaking in Spontaneously

Broken N=2 SQCD

Shin Sasaki(Univ. of Helsinki)

[hep-th/0708.0668 (M.Arai, C.Montonen, N.Okada and S.S)]

Introduction—meta-stable SUSY breaking

Dynamical SUSY breaking

hierarchy problem can be solved

Witten index

highly constrained models are allowed

very restricted models are considered before the discovery of the ISS model

Witten index never restrict the possibility of meta-stable SUSY breaking vacua

[Intriligator-Seiberg-Shih (2006)]

The ISS model

SQCD with massive flavors

IR-free magnetic dual

One-loop up-lifting of pseudo moduli

Long-lived local minimum

Dynamical SUSY restoration

Perturbative regionNon-pertrubative

SUSY restroation

[Intriligator-Seiberg-Shih (2006)]

Ubiquity of meta-stable SUSY breaking

ISS inspired model

Perturbed Seiberg-Witten

Brane constraction

U(1)_R breaking

Gauge mediation, finite temperature ….

[Ooguri-Ookouchi-Park (2007), Pastras (2007)]

[Shih (2007), Ferretti (2007), Intriligator-Seiberg-Shih (2007), …]

[Franco-Garcia-Etxebarria-Uranga (2006), Ahn (2007), Ooguri-Ookouchi (2007),

Eto-Hashimoto-Terashima (2007), Bena-Gorbatov-Hellerman-Seiberg-Shih (2007),

Marsano-Papadodimas-Shigemori (2007) …]

[Amariti-Girardello-Mariotti (2007), Essig-Sinha-Torroba (2007),

Abel-Khoze (2007), …]

[Kawano-Ooguri-Ookouchi (2007), Murayama-Nomura (2007),Aharony-Seiberg (2007),

Kitano-Ooguri-Ookouchi (2007), …]

Plan of this talk

Introduction

Spontaneously broken N=2 SQCD

Quantum theory

Local minimum – numerical analysis

Possible application to phenomenology

Summary and future works

Spontaneous broken N=2 SQCD

gauge theory with hypermultiplets

and FI-term (D-term)

The simplest case

Global symmetry

Pseudo flat direction

Solution of stationary condition of the potential

SUSY is broken at tree-level

Pseudo flat direction

Gauge symmetryU(1)_R is broken

Quantum theory

Effective action

FI term is tree-level exact [Arai-Kitazawa (1999)]

Harmonic superspace analysis, gauge symmetry, U(1)_R charge….

Coulomb branch

U(1) gauge theory cutoff theory, Landau pole

Seiberg-Witten analysis, Long-lived local minimum

[Arai-Okada (2001)]

SUSY effective action

Vector multiplet part

Light BPS states around singular points

M corresponds to dyons, monopoles, quarks

Spinor representation of[Seiberg-Witten (1994)]

Prepotential

Moduli spaceMonodoromy transf. subgroup of

Same structure with massive SQCD (common quark hypermultiplet mass)

is regarded as the mass

Potential

Stationary points

Singular points : energetically favored !

Solution

SW curve

Meromorphic differential

Periods

Explicit form (Weierstrass functions, elliptic integrals)

U(1) sector

Local mininum

Flow of singularities

Dyon points

Increasing direction

Re(a_1) direction

Im(a_1) direction

Local mininum at a_1 = 0

Local minimum at

SUSY and global U(1)_R are broken !

Local minimum SUSY breaking and U(1)_R breaking

Runaway direction

Decay rate estimate

Long-lived vacuum

[Dancan-Jensen (1992)]

Application to phenomenology

SUSY breaking effect gauge mediation

Messenger sector

Gaugino mass

Singular point in moduli space (meta-stable vacuum)

Summary

gauge theory with hypermultiplets and FI-term

We have found a meta-stable vacuum in which SUSY and U(1)_R are dynamically broken (non-perturbative)Long-lived local minimum with runaway SUSY vacuumThe model naturally contains messenger sector of gauge mediation

Future works

Generalize to arbitrary

Geometric realization of the meta-stable vacua : NS5/D4/(D6) M5 (with TN)

Embedding the Standard Model gauge symmetry into the flavor symmetry

Finite temperature correction