Nonperturbative Recursion Relations in N=2 Supersymmetric Gauge Theories

TL;DR

This paper derives nonperturbative recursion relations for instanton corrections in N=2 supersymmetric gauge theories, enabling systematic computation of high-order corrections based on Seiberg-Witten solutions.

Contribution

It introduces new recursion relations for instanton corrections in N=2 theories with various hypermultiplet configurations, advancing the computational methods for these models.

Findings

Derived recursion relations for instanton corrections

Validated results against existing literature

Facilitated high-order instanton calculations

Abstract

Linear recursion relations for the instanton corrections to the effective prepotential are derived for two cases of N=2 supersymmetric gauge theories; the first case with an arbitrary number of hypermultiplets in the fundamental representation of an arbitrary classical gauge group, and the second case with one hypermultiplet in the adjoint representation of SU(N). The construction for both cases proceed from the Seiberg-Witten solutions and the renormalization group type equations for the prepotential. Successive iterations of these recursion relations allow us to simply obtain instanton corrections to an arbitrarily high order. Checks with previous results in the literature were performed. Other theoretical properties and generalizations are also discussed.