Prepotential Recursion Relations in N=2 Super-Yang Mills with Adjoint Matter

TL;DR

This paper derives recursion relations for instanton corrections in N=2 supersymmetric SU(N) gauge theories with adjoint matter, using Calogero-Moser parameterization, and explores S-duality and spectral curve generalizations.

Contribution

It introduces linear recursion relations for the prepotential's instanton corrections in N=2 theories with adjoint matter, extending to arbitrary simply laced groups.

Findings

Derived recursion relations for instanton corrections

Discussed S-duality properties of the spectral curves

Proposed generalizations to other gauge groups

Abstract

Linear recursion relations for the instanton corrections to the effective prepotential are derived for N=2 supersymmetric gauge theories with one hypermultiplet in the adjoint representation of SU(N) using the Calogero-Moser parameterization of the Seiberg-Witten spectral curves. S-duality properties of the Calogero-Moser parameterization and conjectures on the Seiberg-Witten spectral curves generalized to arbitrary simply laced classical gauge groups are also discussed.