Mass Perturbations in Twisted N=4 Supersymmetric Gauge Theories

TL;DR

This paper investigates mass perturbations in twisted N=4 supersymmetric gauge theories on Kahler four-manifolds, demonstrating invariance of the partition function and linking the perturbation to an equivariant extension related to a U(1) symmetry.

Contribution

It introduces a new perspective on mass perturbations as equivariant extensions tied to U(1) symmetry in Kahler manifolds, preserving the partition function.

Findings

Mass perturbations can be viewed as equivariant extensions.

Partition function remains invariant under mass perturbations.

The approach applies specifically to Kahler four-manifolds.

Abstract

Mass perturbations of the twisted N=4 supersymmetric gauge theory considered by Vafa and Witten to test S-duality are studied for the case of Kahler four-manifolds. It is shown that the resulting mass-perturbed theory can be regarded as an equivariant extension associated to a U(1) symmetry of the twisted theory, which is only present for Kahler manifolds. In addition, it is shown that the partition function, the only topological invariant of the theory, remains invariant under the perturbation.