LOCAL BRST COHOMOLOGY IN EINSTEIN-YANG-MILLS THEORY

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 (normal) actions. The analysis is carried out in spacetimes with R(n) topology, for all spacetime dimensions strictly 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 module 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 related to the non-triviality of the manifold of the gravitational variables. 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, i.e. they can be chosen to be invariant under local Lorentz and Yang-Mills transformations and covariant under diffeomorphisms, with a few exceptions discussed as well.