Non-perturbative treatment of the linear covariant gauges by taking into account the Gribov copies

TL;DR

This paper develops a non-perturbative approach to linear covariant gauges by restricting the functional integral to eliminate Gribov copies, leading to a refined gluon propagator consistent with lattice simulations.

Contribution

It introduces a local effective action for linear covariant gauges that accounts for Gribov copies, extending the Gribov-Zwanziger framework beyond Landau gauge.

Findings

Derived a local form of the effective action with auxiliary fields.

Identified dimension two condensates at the quantum level.

Obtained a tree-level gluon propagator compatible with lattice data.

Abstract

In this paper, a proposal for the restriction of the Euclidean functional integral to a region free of infinitesimal Gribov copies in linear covariant gauges is discussed. An effective action, akin to the Gribov-Zwanziger action of the Landau gauge, is obtained which implements the aforementioned restriction. Although originally non-local, this action can be cast in local form by introducing auxiliary fields. As in the case of the Landau gauge, dimension two condensates are generated at the quantum level, giving rise to a refinement of the action which is employed to obtain the tree-level gluon propagator in linear covariant gauges. A comparison of our results with those available from numerical lattice simulations is also provided.