Global issues in gauge fixing

TL;DR

This paper reviews global gauge fixing issues and their impact on glueball spectroscopy, emphasizing how finite volume formulations reveal the sensitivity of low-lying states to gauge copies and topological features.

Contribution

It introduces a finite volume approach to study gauge fixing ambiguities and their effects on glueball wave functionals, highlighting the role of geometry and topology.

Findings

Low-lying states are sensitive to gauge copies.

Finite volume formulations help avoid infrared singularities.

Wave functionals reflect geometric and topological features.

Abstract

We review the global issues associated to gauge fixing ambiguities and their consequence for glueball spectroscopy. To avoid infrared singularities the theory is formulated in a finite volume. The examples of a cubic and spherical geometry will be discussed in some detail. Our methods are not powerful enough to study the infinite volume limit, but the results clearly indicate that for low-lying states, wave functionals are sensitive to global gauge copies which we will argue is equivalent to saying that they are sensitive to the geometric and topological features of configuration space.