BRST Symmetries for the Tangent Gauge Group

TL;DR

This paper develops BRST symmetries for tangent gauge groups in principal bundles, extending quantum field theory frameworks to include tangent vectors of connections and curvatures, with applications to BF-Yang-Mills and topological BF theories.

Contribution

It introduces BRST operators for fields in the tangent bundle of the connection space and analyzes their application to BF-Yang-Mills and topological BF theories.

Findings

BRST symmetry for tangent gauge groups is formulated.

Gauge fixing conditions for BF-Yang-Mills are analyzed.

Batalin-Vilkovisky operator for topological BF theories is described.

Abstract

For any principal bundle $P$, one can consider the subspace of the space of connections on its tangent bundle $TP$ given by the tangent bundle $T{\cal A}$ of the space of connections ${\cal A}$ on $P$. The tangent gauge group acts freely on $T{\cal A}$. Appropriate BRST operators are introduced for quantum field theories that include as fields elements of $T{\cal A}$, as well as tangent vectors to the space of curvatures. As the simplest application, the BRST symmetry of the so-called $BF$-Yang-Mills theory is described and the relevant gauge fixing conditions are analyzed. A brief account on the topological $BF$ theories is also included and the relevant Batalin-Vilkovisky operator is described.