The other topological twisting of N=4 Yang-Mills

TL;DR

This paper introduces an alternative topological twist of N=4 Yang-Mills theory where the path integral is governed by flat connections of the complexified gauge group, revealing a new invariant on certain four-manifolds.

Contribution

It presents a novel topological twist of N=4 Yang-Mills theory focusing on flat connections, expanding the understanding of topological invariants in four-manifold theory.

Findings

Path integral dominated by flat connections of complexified gauge group

Applicable to non-simply connected four-manifolds with nonpositive Euler number

Defines a new topological invariant analogous to the Casson invariant

Abstract

We present the alternative topological twisting of N=4 Yang-Mills, in which the path integral is dominated not by instantons, but by flat connections of the COMPLEXIFIED gauge group. The theory is nontrivial on compact orientable four-manifolds with nonpositive Euler number, which are necessarily not simply connected. On such manifolds, one finds a single topological invariant, analogous to the Casson invariant of three-manifolds.