Background Effective Action with Nonlinear Massive Gauge Fixing

TL;DR

This paper develops a BRST-invariant, nonlinear massive gauge fixing formalism within the background field approach, enabling consistent quantum gauge theories with nonperturbative insights like gluon condensates.

Contribution

It introduces a novel background field formalism with BRST-invariant mass parameters and nonlinear gauge fixing, preserving invariances and enabling nonperturbative analysis.

Findings

Preserves background and BRST invariance in gauge fixing.

Computes one-loop effective action and beta function.

Provides evidence for gluon condensate formation.

Abstract

We combine a recent construction of a BRST-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the corresponding beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one-loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter.