Gauge Orbits and the Coulomb Potential

TL;DR

This paper explores the relationship between two criteria for Coulomb confinement in gauge theories, linking the vanishing of timelike link variables in Coulomb gauge to the spectrum of the Faddeev-Popov operator through a geometric perspective.

Contribution

It establishes a connection between the Coulomb confinement criterion based on link variables and the spectrum of the Faddeev-Popov operator, providing a geometric interpretation.

Findings

Connected the two Coulomb confinement criteria.

Provided a geometric basis for the relationship.

Clarified implications for gauge theory confinement.

Abstract

If the color Coulomb potential is confining, then the Coulomb field energy of an isolated color charge is infinite on an infinite lattice, even if the usual UV divergence is lattice regulated. A simple criterion for Coulomb confinement is that the expectation value of timelike link variables vanishes in Coulomb gauge, but it is unclear how this criterion is related to the spectrum of the corresponding Faddeev-Popov operator, which can be used to formulate a quite different criterion for Coulomb confinement. The purpose of this article is to connect the two seemingly different Coulomb confinement criteria, and explain the geometrical basis of the connection.