Extended BRST invariance in topological Yang Mills theory revisited

TL;DR

This paper explores the structure of extended BRST invariance in topological Yang-Mills theory, demonstrating how a field redefinition can reconcile asymmetric gauge fixings with symmetric extended BRST algebra at the non-interacting level.

Contribution

It shows that a simple field redefinition can produce the gauge fixing action of topological Yang-Mills theory from an extended BRST algebra with symmetric ghost-antighost spectrum.

Findings

A field redefinition aligns gauge fixing with symmetric extended BRST algebra.

Not all gauge fixings in topological Yang-Mills are obtainable from symmetric extended BRST algebra.

The approach applies at the non-interacting level.

Abstract

Extended BRST invariance (BRST plus anti-BRST invariances) provides in principle a natural way of introducing the complete gauge fixing structure associated to a gauge field theory in the minimum representation of the algebra. However, as it happens in topological Yang Mills theory, not all gauge fixings can be obtained from a symmetrical extended BRST algebra, where antighosts belong to the same representation of the Lorentz group of the corresponding ghosts. We show here that, at non interacting level, a simple field redefinition makes it possible to start with an extended BRST algebra with symmetric ghost antighost spectrum and arrive at the gauge fixing action of topological Yang Mills theory.