Local BRST cohomology in Einstein--Yang--Mills theory

TL;DR

This paper thoroughly analyzes the local BRST cohomology in Einstein-Yang-Mills theory across all spacetime dimensions, classifying anomalies and deformations, and revealing how gauge invariance constrains possible modifications.

Contribution

It extends the classification of anomalies and deformations in Einstein-Yang-Mills theory by allowing general invariant actions and analyzing antifield dependence across all dimensions.

Findings

Antifield dependence can be removed for semi-simple gauge groups.

Allowed deformations preserve gauge structure.

Candidate anomalies include known and topological anomalies in specific dimensions.

Abstract

We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general diffeomorphism and gauge invariant actions. The analysis is carried out in all spacetime dimensions larger than 2 and for all ghost numbers. This covers the classification of all candidate anomalies, of all consistent deformations of the action, as well as the computation of the (equivariant) characteristic cohomology, i.e. the cohomology of the spacetime exterior derivative in the space of (gauge invariant) local differential forms modulo forms that vanish on-shell. We show in particular that for a semi-simple Yang-Mills gauge group the antifield dependence can be entirely removed both from the consistent deformations of the Lagrangian and from the candidate anomalies. Thus, the allowed deformations of the action necessarily preserve the gauge structure, while the only candidate anomalies are those provided by previous works not dealing with antifields, and by ``topological" candidate anomalies which are present only in special spacetime dimensions (6,9,10,13,...). This result no longer holds in presence of abelian factors where new candidate anomalies and deformations of the action can be constructed out of the conserved Noether currents (if any). The Noether currents themselves are shown to be covariantizable, with a few exceptions discussed as well.