Constrained Hamiltonian structure of the chirally gauged Wess-Zumino-Witten model

Abstract

We construct the canonical formulation of the left-gauged non-Abelian Wess-Zumino-Witten (WZW) model in four dimensions using Dirac's method of constraints. This study is motivated by our interest in establishing the canonical consistency of anomalous non-Abelian gauge theories of chiral fermions, which are believed to be approximated by the corresponding WZW action in the low energy limit. We introduce in the action a free parameter α, reflecting some of the regularization ambiguities of the anomaly. We find that for α > 1, the WZW model is classically consistent and has a unique positive Hamiltonian, suggesting that the corresponding anomalous fermionic theory will also be consistent and unitary. The case α = 1 is also studied and is shown to have some remarkable properties. Finally, some implications of our results for the Faddeev-Shatashvili model are pointed out.