Meta-stable Supersymmetry Breaking in an N=1 Perturbed Seiberg-Witten Theory Shin Sasaki (Univ. of Helsinki, Helsinki Inst. of Physics) Phys. Rev. D76 (2007) , arXiv: [hep-th]arXiv: [hep-th] JHEP 03 (2008) 004, arXiv: [hep-th]arXiv: [hep-th] (M.Arai, C.Montonen, N.Okada and S.S)

Dynamical SUSY breaking  hierarchy problem can be solved [Witten (1981)] Witten index – # of SUSY vacua in a model [Witten (1982)]  very restricted models have been considered before the discovery of the ISS model  meta-stable SUSY breaking vacua Introduction Meta-stable SUSY breaking? [Intriligator-Seiberg-Shih (2006)] N=2 SQCD  non-perturbative analysis is possible SQCD

Four-dimensional N=2 SQCD with FI term perturbation Massless fundamental hypermultiplets, preserves N=2 SUSY Gauge group is Simple case  Quantum Theory – Seiberg-Witten analysis [Seiberg-Witten (1994)] There is a meta-stable SUSY breaking vacuum at the dyon singular point in the moduli space Exact effective potential can be obtained and stational point was analyzed [Arai-Montonen-Okada-S.S, arXiv: [hep-th]]

The model [Arai-Montonen-Okada-S.S, arXiv: [hep-th]]

N=1 preserving adjoint scalar mass deformation to N=2 SQCD Classical SUSY vacua on the Coulomb branch Classical SUSY vacua on the Higgs branch

Quantum theory Modulus Coulomb branch in vanishing FI term U(1) gauge theory  cutoff theory, Landau pole [Arai-Okada (2001)] U(1) part is always weak  Moduli space is constrained

Vector multiplet part Hypermultiplets  Light BPS states around singular points in moduli space M corresponds to dyons, monopoles, quarks SUSY preserving part

Stational points in Hypermultiplet directions Energies corresponding to these solutions are  Energetically favored at singular points in the moduli space This solution is stable in M directions Let us find out stational point in the directions  Explicit form of the metric on the moduli space is needed The potential is a function

9 Moduli space Monodoromy transf.  subgroup of  Same structure with SU(2) massive SQCD (common quark hypermultiplet mass) Prepotential  Metric of the moduli space is determined C is a free parameter which defines the Landau pole scale [Arai-Okada (2001)]  The structure of the potential is completely determined can be regarded as the mass

Now, the potential is a function of which has been minimized in the directions due to the non-zero condensation of monopoles, dyons, quarks. In the moduli space, the singular points are completely determined by the cubic polynomial [Seiberg-Witten (1994)]  There is a relation between and at each singular points  At the singular points, the potential is a function of only! There are three singularities in our model (dyons, monople, quark)

Degenerate dyon and monopole Left and right dyons and quark Flow of singularities (real part of ) Flow of singularities for complex is essentially the same with

First, consider case Numerical analysis

13 Potential behavior around the monopole singular point Potential plot Complex SUSY vacuum at

Potential around dyon singular points  SUSY vacuum at

Global structure of the potential, case monopole Left, right dyons right dyon quark SUSY vacua SUSY vacua at at dyons and monopole points

Turn on

Izawa-Yanagida-Intriligator-Thomas (IYIT) mechanism If we turn on which produce a vacuum at a point different from as SUSY vacua, the full effective action would contain SUSY breaking vacua This is similar to the Izawa-Yanagida-Intriligator-Thomas (IYIT) model U(1) part is essential in our model [Izawa-Yanagida (1996), Intriligator-Thomas (1996)]

Potential behavior at monopole singular point, case Two SUSY breaking local minima at the degenerated dyon and monopole singular points The behavior of the degenerate dyon singular point is the same with the monopole one  symmetry

Global structure of the full potential Meta-stable SUSY breaking minima

Decay rate estimation Higgs branch  no quantum corrections  Classical SUSY vacua remains intact The bounce action can be estimated from the classical potential can be taken to be large  meta-stable vacua Coulomb branch Higgs branch

gauge theory with hypermultiplets perturbed by adjoint mass and FI-terms We have found meta-stable SUSY breaking vacua in the non-perturbative effective potential via the Seiberg-Witten analysis Long-lived local minimum The SUSY breaking mechanism presented here is similar to the one in the IYIT model Generalization to arbitrary by the help of brane configurations Summary and perspective