Akin $N=2$ SUSY Yang Mills Theories and Instanton Expansion

Abstract

The low energy effective actions of the $N=2$ SUSY $SU(N_c)$ QCD are considered at the symmetric point on the moduli space. The classes of such theories have similar spectral curves. This fact allows us to show that all these models have the same structure of the coupling matrix and to show that the $N_f=2N_c$ spectral curve can not be presented as a double covering of the sphere. We calculate first instanton contributions to the coupling matrix and get nonperturbative $β$-functions in the $SU(2)$ gauge theory with non-zero bare masses of the matter hypermultiplets.