The Witten Index Revisited

TL;DR

This paper revisits the Witten index in supersymmetric gauge theories, addressing orbifold singularities in the moduli space of flat connections on a torus by imposing boundary conditions to eliminate gauge copies.

Contribution

It introduces a method to handle orbifold singularities in the moduli space through boundary conditions, refining the calculation of the Witten index.

Findings

Orbifold singularities can be managed with specific boundary conditions.

The approach improves the understanding of the moduli space structure.

Results clarify the role of boundary conditions in supersymmetric gauge theories.

Abstract

We attempt to deal with the orbifold singularities in the moduli space of flat connections for supersymmetric gauge theories on the torus. The fields are restricted to the fundamental domain, containing no gauge copies, but requiring a boundary condition in field space.