A simple perturbation of Vafa-Witten equations and a transversality result

TL;DR

This paper introduces a straightforward perturbation of the Vafa-Witten equations and demonstrates that, for generic parameters, the moduli space achieves transversality when the structure group is SU(2) or SO(3).

Contribution

It provides a new perturbation method ensuring transversality of the Vafa-Witten moduli space for specific gauge groups.

Findings

Transversality holds for generic perturbations.

Results apply to SU(2) and SO(3) gauge groups.

Ensures smoothness of the moduli space under perturbation.

Abstract

We consider a simple perturbation of the Vafa-Witten equations, and prove that for generic perturbation parameter, the full rank part of the perturbed Vafa-Witten moduli space satisfies transversality condition, when the structure group is $SU(2)$ or $SO(3)$.