Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

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 differentials modulo the exterior space-time derivatived 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 conditionssa+db=0 depending non-trivially on the antifields are exhibited. For a semi-simple 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 conditionsa+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.Supported by Deutsche Forschungsgemeinschaft and by the research council (DOC) of the K.U. Leuven.