Revisiting Gribov's Copies Inside The Horizon

TL;DR

This paper investigates the existence of topologically trivial Gribov copies within the Gribov horizon, providing explicit examples and analyzing the influence of non-trivial backgrounds like Polyakov instantons on their generation.

Contribution

It introduces a new method to construct valid Gribov copies avoiding previous reducibility issues and applies it to backgrounds with Polyakov instantons.

Findings

Constructed explicit spherical symmetric Gribov copies.

Demonstrated the effect of Polyakov instantons on multiple copies.

Provided insights into the structure of gauge copies inside the horizon.

Abstract

In this work, we recover the problem of legitimate topologically trivial Gribov copies inside the Gribov horizon. We avoid the reducibility problem which hampered the standard construction of van Baal, and then we are able to build a valid example with spherical symmetry. We also apply the same technique in the presence of a background of a Polyakov instanton in a Euclidian 3D spacetime, in order to study the effect of a non trivial environment in the generation of multiple copies inside the horizon.