Coulomb gauge Gribov copies and the confining potential

TL;DR

This paper investigates the impact of Gribov copies on the Coulomb gauge approach to the static quark potential, demonstrating how averaging over copies preserves gauge invariance and allows for accurate potential calculations at all distances.

Contribution

It introduces a method to maintain gauge invariance by averaging over Gribov copies, enabling a consistent analysis of the static potential across all distance scales.

Findings

Averaging over Gribov copies preserves gauge invariance.

The interpolating state accurately reproduces the static potential.

The approach works effectively at all distances.

Abstract

We study the approach, initiated by Marinari et al., to the static inter-quark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant colour charges. At larger separations Gribov copies obstruct the non-perturbative identification of individually gauge invariant colour states. We demonstrate, for the first time, how gauge invariance can be maintained quite generally by averaging over Gribov copies. This allows us to extend the analysis of the Polyakov lines and the corresponding, gauge invariant quark-antiquark state to all distance scales. Using large scale lattice simulations, we show that this interpolating state possesses a good overlap with the ground state in the quark-antiquark sector and yields the full static inter-quark potential at all distances. A visual representation of the Gribov copies on the lattice is also presented.