On metastable vacua in perturbed N=2 theories

Abstract

We study supersymmetry breaking in metastable vacua on the Coulomb branch of perturbed N=2 gauge theories, with gauge group SU(2) and different matter content (N_f=0,2,4). The theory is deformed with a superpotential which is a cubic polynomial in u=Tr \Phi ^2, where \Phi is the adjoint superfield. The allowed region of the perturbation parameters in this N=1 theory is plotted as a function of the moduli space coordinate. In the asymptotically free cases a significant fine-tuning in the perturbation parameters is needed to achieve metastable vacua in the weakly coupled region of the moduli space; a lower degree of fine-tuning is required in the strongly coupled regime. In the conformal case (N_f=4 fundamentals) we find that also an explicit mass for the hypermultiplets must be introduced in order to generate metastable vacua. In the case of N_f=2 fundamentals it is possible to achieve a metastable vacuum also in the neighborhood of the Argyres-Douglas fixed point (even if a large degree of fine-tuning is needed in this limit). Direct gauge mediation is discussed; gaugino masses of the same order of the SUSY-breaking can be obtained.