Instanton Recursion Relations for the Effective Prepotential in N=2 Super Yang-Mills

TL;DR

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

Contribution

It introduces a new recursive method to compute instanton corrections to the prepotential for arbitrary gauge groups and hypermultiplet content, extending previous results.

Findings

Explicit 6th order instanton corrections obtained

Results agree with known cases for SU(2) and SU(3)

Recursion relations simplify high-order instanton calculations

Abstract

Linear recursion relations for the instanton corrections to the effective prepotential of N=2 supersymmetric gauge theories with an arbitrary number of hypermultiplets in the fundamental representation of an arbitrary classical gauge group are dervied. The construction proceeds from the Seiberg-Witten solutions and the renormalization group type equations for the prepotential. Successive iterations of these recursion relations allow us to simple obtain instanton corrections to arbitrarily high order, which we exhibit explicitly up to 6-th order. For gauge groups SU(2) and SU(3), our results agree with previous ones.