Duality in twisted N=4 supersymmetric gauge theories in four dimensions

TL;DR

This paper computes the partition function and correlation functions of a twisted N=4 supersymmetric gauge theory in four dimensions, analyzing duality properties and confirming S-duality predictions on specific four-manifolds.

Contribution

It introduces a method to compute topological invariants of twisted N=4 theories with mass deformations and analyzes their duality transformations, extending previous results.

Findings

Partition function matches Vafa-Witten's result on K3.

Correlation functions transform covariantly under duality.

The formulae exhibit expected S-duality behavior.

Abstract

We consider a twisted version of the four-dimensional N=4 supersymmetric Yang-Mills theory with gauge groups SU(2) and SO(3), and bare masses for two of its chiral multiplets, thereby breaking N=4 down to N=2. Using the wall-crossing technique introduced by Moore and Witten within the u-plane approach to twisted topological field theories, we compute the partition function and all the topological correlation functions for the case of simply-connected spin four-manifolds of simple type. By including 't Hooft fluxes, we analyse the properties of the resulting formulae under duality transformations. The partition function transforms in the same way as the one first presented by Vafa and Witten for another twist of the N=4 supersymmetric theory in their strong coupling test of S-duality. Both partition functions coincide on K3. The topological correlation functions turn out to transform covariantly under duality, following a simple pattern which seems to be inherent in a general type of topological quantum field theories.