The Regularized BRST Jacobian of pure Yang-Mills theory

Abstract

The Jacobian for infinitesimal BRST transformations of path in-tegrals for pure Yang-Mills theory, viewed as a matrix 1 + Jin the space of Yang-Mills fields and (anti)ghosts, contains off-diagonal terms. Naively, the trace of J vanishes, being propor-tional to the trace of the structure constants. However, the con-sistent regulator R, constructed from a general method, also con-tains off-diagonal terms. An explicit computation demonstratesthat the regularized Jacobian Tr J exp−R/M2 for M2 → ∞ is the variation of a local counterterm, which we give. This is adirect proof at the level of path integrals that there is no BRSTanomaly.