LOCAL BRST COHOMOLOGY IN THE ANTIFIELD FORMALISM .2. APPLICATION TO YANG-MILLS THEORY

Yang-Mills models with compact gauge group coupled to matter fields ar e considered. The general tools developed in a companion paper are app lied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost numbe r, in the space of polynomials in the fields, the ghosts, the antifiel ds (=sources for the BRST variations) and their derivatives. New solut ions to the consistency conditions sa + db = 0 depending non-trivially on the antifields are exhibited. For a semi-simple gauge group, howev er, 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 besid es the already known ones. The analysis does not use power counting an d is purely cohomological. It call be easily extended to more general actions containing higher derivatives of the curvature or Chern-Simons terms.