Some Non-Perturbative Aspects of Gauge Fixing in Two Dimensional Yang-Mills Theory

Gauge fixing in general is incomplete, such that one solves some of the gauge constraints, quantizes, then imposes any residual gauge symmetries (Gribov copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of the local metric on this gauge fixed surface, the global topology of the reduced configuration space can be different depending on the treatment of the residual symmetries, which can in turn affect global properties of the theory such as the vacuum wavefunction. Pure $SU(N)$ gauge theory in two dimensions provides a simple yet non-trivial example where the above structure and effects can be elucidated explicitly, thus displaying physical effects of the treatment of Gribov copies.