Path integral formulation of the conformal Wess-Zumino-Witten → Toda reductions Original Research Article

The phase space path integral Wess-Zumino-Witten → Toda reductions are formulated in a manifestly conformally invariant way. For this purpose, the method of Batalin, Fradkin, and Vilkovisky, adapted to conformal field theories, with chiral constraints, on compact two-dimensional Riemannian manifolds, is used. It is shown that the zero-modes of the Lagrange multipliers produce the Toda potential and the gradients produce the WZW anomaly. This anomaly is crucial for proving the Fradkin-Vilkovisky theorem concerning gauge invariance.