AntiBRST symmetry and Background Field Method

TL;DR

This paper demonstrates that invariance under both BRST and antiBRST symmetries in SU(N) Yang-Mills theory naturally leads to the background field method, revealing its fundamental role without additional assumptions.

Contribution

It shows that the background field method arises automatically from antiBRST invariance, unifying gauge fixing and symmetry principles in Yang-Mills theories.

Findings

BFM and background Ward identity emerge from antiBRST invariance

Ghost and antighost sectors are algebraically resolved

Background fields are stationary points of the effective action

Abstract

We show that the requirement that a SU(N) Yang-Mills action (gauge fixed in a linear covariant gauge) is invariant under both the Becchi-Rouet-Stora-Tyutin (BRST) symmetry as well as the corresponding antiBRST symmetry, automatically implies that the theory is quantized in the (linear covariant) background field method (BFM) gauge. Thus, the BFM and its associated background Ward identity naturally emerge from antiBRST invariance of the theory and need not be introduced as an ad hoc gauge fixing procedure. Treating ghosts and antighosts on an equal footing, as required by a BRST-antiBRST invariant formulation of the theory, gives also rise to a local antighost equation that together with the local ghost equation completely resolve the algebraic structure of the ghost sector for any value of the gauge fixing parameter. We finally prove that the background fields are stationary points of the background effective action obtained when the quantum fields are integrated out.