Covariant W gravity and its moduli space from gauge theory

Abstract

In this paper we study arbitrary classical W algebras related to embeddings of sl 2 in a Lie algebra g. We will give a simple general formula for all W transformations, which will enable us to construct the covariant action for general classical W gravity. It turns out that this covariant action is nothing but a Legendre transform of the WZW action. The same general formula provides a “geometrical” interpretation of W transformations: they are just a homotopy contraction of ordinary gauge transformations. This is used to argue that the moduli space relevant to W gravity is part of the moduli space of G-bundles over a Riemann surface.