Ground states of supersymmetric Yang-Mills-Chern-Simons theory

TL;DR

This paper calculates the ground states of supersymmetric Yang-Mills-Chern-Simons theory on a two-torus using moduli space localization, confirming previous results and enabling detailed analysis of electric fluxes.

Contribution

It introduces a new method of computing the Witten index via orbifolded moduli space, simplifying the determination of electric 't Hooft fluxes in non-simply connected gauge groups.

Findings

Results agree with previous complex projective space approach.

Method allows straightforward determination of discrete electric fluxes.

Invariance under the three-torus mapping class group is confirmed.

Abstract

We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus. The Witten index may be computed in the weak coupling limit, where the ground state wave-functions localize on the moduli space of flat gauge connections. We perform such computations by considering this moduli space as an orbifold of a certain flat complex torus. Our results agree with those obtained previously by instead considering the moduli space as a complex projective space. An advantage of the present method is that it allows for a more straightforward determination of the discrete electric 't Hooft fluxes of the ground states in theories with non-simply connected gauge groups. A consistency check is provided by the invariance of the results under the mapping class group of a (Euclidean) three-torus.