Recurrence relation for instanton partition function in SU(N) gauge theory

TL;DR

This paper derives a generalized recurrence relation for the equivariant instanton partition function in SU(N) gauge theories, extending previous results to include matter hypermultiplets and different representations.

Contribution

It introduces a unified recurrence relation for instanton partition functions in SU(N) theories with various matter content, broadening the understanding of their structure.

Findings

Derived a general recurrence relation for SU(N) instanton partition functions

Extended the relation to theories with matter hypermultiplets

Provided a framework applicable to pure and matter-coupled theories

Abstract

We study the equivariant instanton partition function in $\mathcal{N}=2$ supersymmetric theory on $\mathbb{C}^2$ with $SU(N)$ gauge group and find the generalisation of the Zamolodchikov recurrence relation. We consider the pure theory as well as theories with matter hypermultiplets in the adjoint and fundamental representations.