Non-trivial Backgrounds in (non-perturbative) Yang-Mills Theory by the Slavnov-Taylor Identity

TL;DR

This paper demonstrates that in Yang-Mills theory, the background field dependence in the BFM is governed by a canonical transformation linked to BRST symmetry, applicable in both perturbative and non-perturbative regimes.

Contribution

It introduces a canonical transformation framework controlling background dependence in the BFM, valid beyond perturbation theory and applicable to non-trivial backgrounds in QCD.

Findings

Background dependence is governed by a canonical transformation.

Framework applies to non-perturbative QCD approaches.

Valid in arbitrary R_xi-gauge.

Abstract

We show that in the background field method (BFM) quantization of Yang-Mills theory the dependence of the vertex functional on the background field is controlled by a canonical transformation w.r.t. the Batalin-Vilkovisky bracket, naturally associated with the BRST symmetry of the theory. Since it only relies on the Slavnov-Taylor identity of the model, this result holds both in perturbation theory and in the non-perturbative regime. It provides a general consistent framework for the systematic implementation of the BFM in non-perturbative approaches to QCD, like e.g. those based on the Schwinger-Dyson equations or the lattice, in the presence of topologically non-trivial background configurations. The analysis is carried out in an arbitrary (background) R_\xi-gauge.