Covariant and consistent anomalies in even-dimensional chiral gauge theories

Abstract

This paper is devoted to various aspects of anomalies in even-dimensional chiral gauge theories. The difference between the covariant and consistent anomalies is carefully explained in terms of their different origins. The consistent current is defined in terms of a gauge-variant effectve action constructed from the covariant current. An alternative scheme is set up where the covariant anomaly is unaltered but the consistent anomaly vanishes because the effective actions is gauge-invariant. A discussion of theories with vector and axial currents separately gauged is included: here, apart from the covariant anomalies, two different ways of constructing gauge-variant effective actions are possible, giving rise to different structures of the consistent anomalies.