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

TL;DR

This paper develops a conformally invariant path integral framework for the Wess-Zumino-Witten to Liouville reduction, explicitly maintaining conformal symmetry and addressing gauge dependence issues in the reduced theory.

Contribution

It introduces a conformally invariant generalization of phase space path integrals and proves a gauge independence theorem, applicable to all conformally invariant reductions.

Findings

Conformal anomaly is naturally incorporated.

Gauge dependence of the Virasoro algebra center is resolved.

Formalism applies across all dimensions for conformally invariant reductions.

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.