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) 125009, arXiv:0708.0668 [hep-th]JHEP 03 (2008) 004, arXiv:0712.4252 [hep-th]

(M.Arai, C.Montonen, N.Okada and S.S)

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• Dynamical SUSY breakinghierarchy 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

IntroductionMeta-stable SUSY breaking?

[Intriligator-Seiberg-Shih (2006)]

N=2 SQCD non-perturbative analysis is possible

SQCD

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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 vacuumat the dyon singular point in the moduli space

Exact effective potential can be obtained andstational point was analyzed

[Arai-Montonen-Okada-S.S, arXiv:0708.0668 [hep-th]]

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The model[Arai-Montonen-Okada-S.S, arXiv:0712.4252 [hep-th]]

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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

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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

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Vector multiplet part

Hypermultiplets

Light BPS states around singular points in moduli space

M corresponds to dyons, monopoles, quarks

SUSY preserving part

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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 directionsExplicit form of the metric on the moduli space is needed

The potential is a function

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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

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Now, the potential is a function of which has been minimized in thedirections 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)

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Degenerate dyon and monopole

Left and right dyonsand quark

Flow of singularities (real part of )

Flow of singularities for complex is essentially the same with

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First, consider case

Numerical analysis

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Potential behavior around the monopole singular point

Potential plotComplex

SUSY vacuum at

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Potential around dyon singular points

SUSY vacuum at

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Global structure of the potential, case

monopole

Left, right dyons right dyon

quark

SUSY vacua

SUSY vacua atat dyons and monopole points

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Turn on

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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)]

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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 withthe monopole one symmetry

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Global structure of the full potential

Meta-stable SUSY breakingminima

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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

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• 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