Gribov copies and topological charge

TL;DR

This paper investigates the proliferation of Gribov copies with different winding numbers in confining gauge theories, exploring their connection to topological charge, instantons, and confinement mechanisms.

Contribution

It explicitly demonstrates the abundance of Gribov copies with relative winding numbers for localized configurations in Coulomb gauge and discusses their potential link to Minkowski solutions and confinement.

Findings

Proliferation of Gribov copies with relative winding number.

Possible connections between Gribov copies and Minkowski space solutions.

Discussion on the role of instantons in confinement.

Abstract

The existence of Gribov copies is a central feature of the field configuration space of confining gauge theories. In particular a transition between two Gribov copies with relative winding number implies a space-time configuration with topological charge. We explicitly demonstrate the proliferation of Gribov copies with relative winding number, where our focus is on localized (finite norm) configurations in Coulomb gauge. We then discuss the likelihood that some pairs of such copies are connected by Minkowski space solutions. We also comment on the relative importance of instantons and the connection to confinement.