The Witten Index Beyond the Adiabatic Approximation

We attempt to deal with the orbifold singularities in the moduli space of flat connections for supersymmetric gauge theories on the torus. At these singularities the energy gap in the transverse fluctuations vanishes and the resulting breakdown of the adiabatic approximation is resolved by considering the full set of zero-momentum fields. These can not be defined globally, due to the problem of Gribov copies. For this reason we restrict the fields to the fundamental domain, containing no gauge copies, but requiring a boundary condition in field space.