On the elimination of infinitesimal Gribov ambiguities in non-Abelian gauge theories

TL;DR

This paper proposes a novel method to eliminate infinitesimal Gribov ambiguities in non-Abelian gauge theories by softly breaking BRST symmetry through an additional constraint, ensuring consistency with known gauge cases.

Contribution

It introduces a new approach that breaks BRST symmetry softly to remove Gribov ambiguities, applicable to gauges depending only on gauge fields at the classical level.

Findings

Method is consistent with Landau and maximal Abelian gauges.

Approach effectively eliminates infinitesimal Gribov copies.

Applicable to gauges depending solely on gauge fields.

Abstract

An alternative method to account for the Gribov ambiguities in gauge theories is presented. It is shown that, to eliminate Gribov ambiguities, at infinitesimal level, it is required to break the BRST symmetry in a soft manner. This can be done by introducing a suitable extra constraint that eliminates the infinitesimal Gribov copies. It is shown that the present approach is consistent with the well established known cases in the literature, i.e., the Landau and maximal Abelian gauges. The method is valid for gauges depending exclusively on the gauge field and is restricted to classical level. However, occasionally, we deal with quantum aspects of the technique, which are used to improve the results.