W-Strings on Curved Backgrounds

Abstract

We discuss a canonical formalism method for constructing actions describing propagation of W-strings on curved backgrounds. The method is based on the construction of a representation of the W-algebra in terms of currents made from the string coordinates and the canonically conjugate momenta. We construct such a representation for a W3-string propagating in the background metric with one flat direction by using a simple ansatz for the W-generators where each generator is a polynomial of the canonical currents and the vierbeins. In the case of a general background, we show that the simple polynomial ansatz fails, and terms containing the vierbein derivatives must be added.