Extended BRS symmetry in topological field theories

TL;DR

This paper introduces an extended BRS symmetry in topological field theories like BF and Chern-Simons, linking it to vector supersymmetry and enhancing their gauge invariance properties.

Contribution

It proposes a new gauge fixing that extends BRS symmetry to include ghost fields for diffeomorphisms, connecting to vector supersymmetry in topological theories.

Findings

Extended BRS symmetry incorporates ghost fields for diffeomorphisms.

The new gauge fixing preserves invariance under the extended symmetry.

Connection established between extended BRS symmetry and vector supersymmetry.

Abstract

A class of topological field theories like the $BF$ model and Chern-Simons theory, when quantized in the Landau gauge, enjoys the property of invariance under a vector supersymmetry, which is responsible for their finiteness. We introduce a new type of gauge fixing which makes these theories invariant under an extended $BRS$ symmetry, containing a new type of field, the ghost of diffeomorphisms. The presence of such an extension is naturally related to the vector supersymmetry discussed before.