The gauged BRST symmetry

Abstract

We develop a systematic method for constructing the gauged BRST symmetry for any theory. In this framework, the gauged BRST symmetry results as the combination of two basic symmetries of the gauge-fixed theory which one considers: the BRST symmetry and the ghost number symmetry, this latter being promoted to a local one. From this, we can derive a general relation between the BRST and the ghost number Noether currents. We then take advantage of the present method to elaborate on a geometrical algorithm leading to the obtainment of the gauged BRST symmetry for a large class of theories, in arbitrary dimensions of space. These involve systems of antisymmetric tensor gauge fields of arbitrary rank, eventually coupled to gravity. This algorithm allows us to derive algebraically the expressions for the possible consistent anomalies of the BRST Noether current algebras; various examples are explicitly discussed. The gauged BRST symmetry for the free bosonic string is also constructed and used to exhibit the link between the trace anomaly and the nilpotency anomaly of the BRST charge operator. In particular, when the Beltrami parametrization is introduced, we show that the corresponding BRST symmetry can be gauged in a way compatible with the holomorphic factorization. A further use of Ward-Slavnov identities constraining the BRST and ghost number current algebra allows us to recover the well-known local counterterm necessary, at the one-loop level, for rendering the BRST current a good conformal operator.