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

TL;DR

This paper analyzes the structure of low energy effective actions in N=2 supersymmetric SU(N_c) gauge theories, focusing on spectral curves, instanton contributions, and nonperturbative beta functions, revealing new insights into their nonperturbative dynamics.

Contribution

It demonstrates that various N=2 SUSY SU(N_c) theories share similar spectral curve structures and computes first instanton contributions to the coupling matrix and beta functions.

Findings

Spectral curves of these theories are similar, with the exception of the N_f=2N_c case.

The N_f=2N_c spectral curve cannot be expressed as a double cover of the sphere.

First instanton contributions to the coupling matrix and nonperturbative beta functions are calculated.

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 $\beta$-functions in the $SU(2)$ gauge theory with non-zero bare masses of the matter hypermultiplets.