Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories

TL;DR

This paper computes the exact low-energy effective action for N=2 supersymmetric SU(3) gauge theory using hyperelliptic curves, Picard-Fuchs equations, and Appell functions, including instanton corrections.

Contribution

It explicitly determines the effective action for SU(3) N=2 gauge theory using hyperelliptic curves and special functions, extending previous work to a more complex gauge group.

Findings

Explicit low-energy effective action for SU(3) gauge theory.

Calculation of leading instanton corrections.

Expression of gauge coupling in terms of Appell functions.

Abstract

We elaborate on our previous work on N=2 supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for $G=SU(3)$ from the underlying hyperelliptic Riemann surface, and calculate the leading instanton corrections. This is done by solving Picard-Fuchs equations and asymptotically evaluating period integrals. We find that the dynamics of the $SU(3)$ theory is governed by an Appell system of type $F_4$, and compute the exact quantum gauge coupling explicitly in terms of Appell functions.