Nonperturbative effective actions of (N=2)-supersymmetric gauge theories

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.