Gauge copies and the fate of background independence in Yang-Mills theories: a leading order analysis

TL;DR

This paper analyzes the impact of the Gribov prescription on background independence in Yang-Mills theories at one-loop order, revealing non-invariance of the effective action and specific behaviors of gauge and ghost propagators.

Contribution

It provides a one-loop perturbative analysis of Gribov effects on background dependence and propagator behavior in Yang-Mills theories within the Landau-DeWitt gauge.

Findings

Effective action is not background invariant at one-loop.

Gauge propagator has complex conjugate poles similar to trivial background case.

Ghost propagator remains enhanced with a $p^{-4}$ behavior.

Abstract

In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be \textit{not} background invariant, as expected, due to a non-vanishing background contribution. The gauge field propagator has the same form as in the case {where the} background is a trivial field, $i.e.$ with complex conjugate poles, which are modified by the corresponding gap equation. The ghost-anti-ghost propagator still displays its enhanced $\sim p^{-4}$ behavior.