The Vafa-Witten Theory for Gauge Group SU(N)

TL;DR

This paper derives the partition function for the Vafa-Witten twisted $ abla$=4 supersymmetric SU(N) gauge theory on Kähler four-manifolds, accounting for 't Hooft fluxes and prime N, advancing understanding of topological gauge theories.

Contribution

It provides an explicit formula for the partition function of the Vafa-Witten theory with SU(N) gauge group on Kähler four-manifolds, including arbitrary 't Hooft fluxes for prime N.

Findings

Partition function derived for SU(N) Vafa-Witten theory

Inclusion of arbitrary 't Hooft fluxes in the analysis

Results applicable to Kähler four-manifolds with $b^{+}_2>1$

Abstract

We derive the partition function for the Vafa-Witten twist of the $\mathcal{N}=4$ supersymmetric gauge theory with gauge group SU(N) (for prime $N$) and arbitrary values of the 't Hooft fluxes $v\in H^{2}(X,\mathbb{Z}_{N})$ on K\"ahler four-manifolds with $b^{+}_2>1$.