PATH-INTEGRAL FORMULATION OF THE CONFORMAL WESS-ZUMINO-WITTEN-]LIOUVILLE REDUCTION

The quantum Wess-Zumino-Witten --> Liouville reduction is formulated u sing the phase space path integral method of Batalin, Fradkin, and Vil kovisky, adapted to theories on compact two dimensional manifolds. The importance of the zero modes of the Lagrange multipliers in producing the Liouville potential and the WZW anomaly, and in proving gauge inv ariance, is emphasised. A previous problem concerning the gauge depend ence of the Virasoro centre is solved. (C) 1998 Elsevier Science B.V. All rights reserved.