Infrared propagators of Yang-Mills-Chern-Simons theories in linear covariant gauges

TL;DR

This paper investigates the non-perturbative infrared behavior of Yang-Mills-Chern-Simons theories in three dimensions, focusing on gauge fixing, Gribov copies, and phase transitions, while maintaining BRST symmetry and gauge parameter independence.

Contribution

It provides a BRST-invariant analysis of the Gribov problem and phase transitions in Yang-Mills-Chern-Simons theories within linear covariant gauges, including condensate generation.

Findings

Identification of a non-trivial phase structure with confining and deconfining phases.

Restoration of BRST symmetry in the presence of Gribov copies.

Gauge parameter independence of physical results.

Abstract

Recent works have explored non-perturbative effects due to the existence of (infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three Euclidean dimensions. In particular, the removal of such copies modify the gauge field propagator by a self-consistent dynamically generated mass parameter, the Gribov parameter. Due to the interplay with the topological mass introduced by the Chern-Simons term, the propagator features a non-trivial set of phases with poles of different nature, leading to the possible interpretation of a confinfing to deconfining phase transition. Inhere, we restore the BRST symmetry which is softly broken by the elimination of gauge copies and provide a BRST-invariant discussion of such a transition. In order to make clear all physical statements, we deal with linear covariant gauges which contain a gauge parameter and therefore allow for an explicit check of gauge parameter independence of physical results. We also discuss the generation of condensates due to the infrared relevance of infinitesimal Gribov copies.