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

TL;DR

This paper explores the impact of residual gauge symmetries and Gribov copies on the global properties of two-dimensional Yang-Mills theory, revealing how different treatments influence the vacuum structure and topological aspects.

Contribution

It provides an explicit analysis of the non-perturbative effects of gauge fixing and residual symmetries in 2D Yang-Mills theory, highlighting their influence on the theory's global properties.

Findings

Residual gauge symmetries affect the vacuum wavefunction.

Global topology varies with treatment of Gribov copies.

Explicit example in 2D SU(N) gauge theory illustrates these effects.

Abstract

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.