The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories

TL;DR

This paper computes the exact effective prepotential for N=2 supersymmetric SU(N_c) gauge theories with flavors, confirming non-renormalization theorems and explicitly evaluating instanton contributions.

Contribution

It provides a unified derivation of the prepotential from spectral curves, validating its form across different models and including instanton effects.

Findings

Prepotential matches all spectral curve models.

Confirms non-renormalization theorems.

Explicit instanton contributions calculated.

Abstract

We determine the effective prepotential for N=2 supersymmetric SU(N_c) gauge theories with an arbitrary number of flavors N_f < 2N_c, from the exact solution constructed out of spectral curves. The prepotential is the same for the several models of spectral curves proposed in the literature. It has to all orders the logarithmic singularities of the one-loop perturbative corrections, thus confirming the non-renormalization theorems from supersymmetry. In particular, the renormalized order parameters and their duals have all the correct monodromy transformations prescribed at weak coupling. We evaluate explicitly the contributions of one- and two-instanton processes.