Integrating over the Coulomb branch in N=2 gauge theory

TL;DR

This paper explores the mathematical structure of N=2 supersymmetric gauge theories, relating Coulomb branch integrals to Donaldson-Witten theory and extending the framework to higher rank gauge groups.

Contribution

It introduces a new formulation of contact terms and generalizes Coulomb branch integrals to higher rank gauge groups in N=2 gauge theories.

Findings

Relation between Coulomb branch integrals and Donaldson-Witten theory clarified.

New expression for contact terms in N=2 gauge theories provided.

Generalization of integrals to higher rank gauge groups achieved.

Abstract

We review the relation of certain integrals over the Coulomb phase of $d=4$, N=2 SO(3) supersymmetric Yang-Mills theory with Donaldson-Witten theory. We describe a new way to write an important contact term in the theory and show how the integrals generalize to higher rank gauge groups.