The Gribov problem in presence of background field for $SU(2)$ Yang-Mills theory

TL;DR

This paper investigates how a constant non-Abelian background field influences the Gribov problem in SU(2) Yang-Mills theory, revealing that larger background fields reduce the Gribov mass and the impact of Gribov copies.

Contribution

It provides the first explicit analysis of the Gribov problem in the presence of a non-trivial background field in SU(2) Yang-Mills theory, including the derivation of modified Gribov equations.

Findings

The background field affects the Gribov copies equation directly.

Larger background fields lead to smaller Gribov mass parameters.

The relevance of Gribov copies decreases with increasing background field.

Abstract

The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.