Consistency and current algebras of a non-Abelian chiral gauge theory in four dimensions

We present a gauge-symmetric reformulation of anomalous gauge theories and study the symmetry structures of an $\mathrm{SU}(N)$ chiral gauge model in four dimensions. The gauge symmetry is made manifest via the introduction of the Wess-Zumino term, but turns out to be spontaneously broken; correspondingly, the gauge bosons become massive and some nonstandard self-interactions of gauge bosons arise. While the total gauge current, consisting of both fermion and unphysical Wess-Zumino fields, is anomaly free, the gauge anomalies and the Schwinger terms reappear in the fermion chiral currents and are related through the underlying gauge symmetry. Canonical reasoning is given to establish their connection.