PATH-INTEGRAL FORMULATION OF THE CONFORMAL WESS-ZUMINO-WITTEN-]TODA REDUCTIONS

The phase space path integral Wess-Zumino-Witten --> Toda reductions a re formulated in a manifestly conformally invariant way. For this purp ose, the method of Batalin, Fradkin, and Vilko-visky, adapted to confo rmal field theories, with chiral constraints, on compact two-dimension al Riemannian manifolds, is used. It is shown that the zero-modes of t he Lagrange multipliers produce the Toda potential and the gradients p roduce the WZW anomaly. This anomaly is crucial for proving the Fradki n-Vilkovisky theorem concerning gauge invariance. (C) 1998 Elsevier Sc ience B.V.