Consistent quantization and symmetry structure of a non-Abelian chiral gauge theory.

Abstract

The SU(N) chiral Schwinger model with a Wess-Zumino term is studied by use of non-Abelian bosonization, the Becchi-Rouet-Stora formalism, and a dual transformation, and it is confirmed that this model is a sensible quantum theory in a certain range of the anomaly parameter a. The SU(N) gauge symmetry restored by the inclusion of the Wess-Zumino term gets spontaneously broken and the gauge field becomes massive. Left-handed fermions are found to be confined while right-handed fermions remain free and massless. For the specific value a=2, the symmetry of the model enlarges [to a U(N)\ifmmode\times\else\texttimes\fi{}U(N) Kac-Moody symmetry]. It is shown by fermionization of the Wess-Zumino field that for a=2 this model is equivalent to massless two-dimensional QCD (${\mathrm{QCD}}_{2}$) in the sense that they share the same gauge field and the same left-handed fermions. A dual transformation is used to cast the model into an equivalent nonlinear system of scalar fields only, which reveals the particle spectrum of the model.