BRST structure for the mixed Weyl-diffeomorphism residual symmetry

TL;DR

This paper demonstrates how the dressing field method can be integrated with the BRST algebra to systematically handle gauge symmetries and diffeomorphisms in theories like General Relativity and conformal structures.

Contribution

It introduces a compatible framework combining the dressing field method with BRST algebra to address residual symmetries and diffeomorphisms in gauge theories.

Findings

Successfully applied to General Relativity and conformal structures

Provides a geometric interpretation of BRST cohomology in this context

Enables systematic reduction of gauge symmetries with diffeomorphism inclusion

Abstract

In this paper, we show the compatibility of the so-called "dressing field method", which allows a systematic reduction of gauge symmetries, with the inclusion of diffeomorphisms in the BRST algebra of a gauge theory. The robustness of the scheme is illustrated on two examples where Cartan connections play a significant role. The former is General Relativity, while the latter concerns the second-order conformal structure where one ends up with a BRST algebra handling both the Weyl residual symmetry and diffeomorphisms of spacetime. We thereby provide a geometric counterpart to the BRST cohomological treatment used in~\cite{Boulanger1} in the construction of a Weyl covariant tensor calculus.