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 +
J in 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 demonstrates that the regularized Jacobian Tr
J exp−R/M2 for M2 → ∞ is the variation of a local counterterm, which we give. This is a direct proof at the level of path integrals that there is no BRST anomaly.