Lorentz symmetry breaking in a Yang-Mills theory within the Gribov restriction

TL;DR

This paper investigates how Lorentz symmetry breaking, caused by the Carroll-Field-Jackiw term, affects the Gribov problem in a four-dimensional Yang-Mills theory, analyzing the Gribov parameter and propagator poles.

Contribution

It introduces a self-consistent gap equation for the Gribov parameter in the presence of Lorentz symmetry breaking within Yang-Mills theory.

Findings

Derived the gap equation considering Lorentz breaking effects.

Analyzed the impact on the propagator poles.

Provided qualitative insights based on observational bounds.

Abstract

In this paper we take into account the existence of Gribov copies in a four-dimensional Yang-Mills theory in the Landau gauge with an effective Lorentz symmetry breaking, induced by the Carroll-Field-Jackiw (CFJ) term. The self consistent gap equation of the Gribov parameter is properly derived and, provided observational bounds to the amplitude of the CFJ parameter in the $SU(2)$ gauge theory, a qualitative analysis of the Gribov parameter and of the poles of the propagator is developed.