Gauge anomalies in an effective field theory

A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff Λ, beyond which the locality of the theory breaks down. The maximal Λ can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories