Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets

TL;DR

This paper develops a recursive method to compute instanton corrections to the prepotential in N=2 supersymmetric gauge theories with classical gauge groups and fundamental matter, using Riemann theta functions and the Whitham hierarchy.

Contribution

It introduces a new recursive approach leveraging the Whitham hierarchy to efficiently calculate instanton corrections in a broad class of N=2 theories.

Findings

Explicit three-instanton correction formulas provided

Method applicable to all classical gauge groups with fundamental matter

Simplifies computation of prepotential corrections to arbitrary order

Abstract

We compute instanton corrections to the low energy effective prepotential of N=2 supersymmetric theories in a variety of cases, including all classical gauge groups and even number of fundamental matter hypermultiplets. To this end, we take profit of a set of first- and second-order equations for the logarithmic derivatives of the prepotential with respect to the dynamical scale expressed in terms of Riemann's theta-function. These equations emerge in the context of the Whitham hierarchy approach to the low-energy Seiberg--Witten solution of supersymmetric gauge theories. Our procedure is recursive and allows to compute the effective prepotential to arbitrary order in a remarkably straightforward way. General expressions for up to three-instanton corrections are given. We illustrate the method with explicit expressions for several cases.