Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and asymptotically conserved n − 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters can be interpreted as asymptotic Killing vector fields of the background, with asymptotic behaviour determined by a new dynamical condition. A universal formula for asymptotically conserved n − 2 forms in terms of the reducibility parameters is derived. Sufficient conditions for finiteness of the charges built out of the asymptotically conserved n − 2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2-cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, Yang-Mills theory and Einstein gravity.

The general solution of the anomaly consistency condition (Wess-Zumino equation) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge invariant operators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yang-Mills type with non power counting renormalizable couplings has also been worked out in any number of spacetime dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their proofs. This involves computing cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variations of the fields ("antifields") included in the problem. Applications of this computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techniques developed in the Report can be applied to other gauge theories, for which relevant references are given.Comment: 150 pages Latex file, minimal corrections, final versio

We establish general theorems on the cohomology $H^*(s|d)$ of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local $p$-forms depending on the fields and the antifields (=sources for the BRST variations). It is shown that $H^{-k}(s|d)$ is isomorphic to $H_k(\delta |d)$ in negative ghost degree $-k\ (k>0)$, where $\delta$ is the Koszul-Tate differential associated with the stationary surface. The cohomological group $H_1(\delta |d)$ in form degree $n$ is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group $H_k(\delta|d)$ in form degree $n$ is isomorphic to the space of $n-k$ forms that are closed when the equations of motion hold. The groups $H_k(\delta|d)$ $(k>2)$ are shown to vanish for standard irreducible gauge theories. The group $H_2(\delta|d)$ is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups $H^{k}(s|d)$ under the introduction of non minimal variables and of auxiliaryComment: 48 pages LaTeX file, ULB-PMIF-94/06 NIKEF-H 94-13 (minor changes in section 10

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa + db = 0 depending non trivially on the antifields are exhibited. For a semisimple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa + db = 0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.

We analyse in detail the local BRST cohomology in Einstein-YangMills 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, 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.