Conformally Invariant Path Integral Formulation of the Wess-Zumino-Witten $\to$ Liouville Reduction

Abstract

The path integral description of the Wess-Zumino-Witten $\to$ Liouville reduction is formulated in a manner that exhibits the conformal invariance explicitly at each stage of the reduction process. The description requires a conformally invariant generalization of the phase space path integral methods of Batalin, Fradkin, and Vilkovisky for systems with first class constraints. The conformal anomaly is incorporated in a natural way and a generalization of the Fradkin-Vilkovisky theorem regarding gauge independence is proved. This generalised formalism should apply to all conformally invariant reductions in all dimensions. A previous problem concerning the gauge dependence of the centre of the Virasoro algebra of the reduced theory is solved.