W-Strings on Curved Backgrounds

TL;DR

This paper develops a canonical formalism for describing W-string propagation on curved backgrounds, constructing W-algebra representations with polynomial currents and identifying the need for additional terms in general backgrounds.

Contribution

It introduces a method to construct W-string actions on curved backgrounds using a polynomial ansatz and explores the limitations and necessary modifications for general backgrounds.

Findings

Successfully constructs W_3-string representation in a specific background.

Identifies failure of polynomial ansatz in general backgrounds.

Highlights the need for derivative terms of veilbeins in complex 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 W_3-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 veilbeins. In the case of a general background we show that the simple polynomial ansatz fails, and terms containing the veilbein derivatives must be added.