On the Geometry of W_n gravity

TL;DR

This paper explores the geometric structure of W_n gravity by relating Hitchin's generalizations of Teichmuller space to W-gravity, offering a covariant framework and a path integral approach for W-strings.

Contribution

It establishes a connection between Hitchin's spaces and W-gravity Teichmuller spaces, providing a new covariant description and path integral formulation for W-strings.

Findings

Relates Hitchin's spaces to W-gravity Teichmuller spaces

Provides a covariant description of W-gravity

Derives a Polyakov path integral prescription for W-strings

Abstract

We report work done with T. Jayaraman (hep-th/9405146) in this talk. In a recent paper, Hitchin introduced generalisations of the Teichmuller space of Riemann surfaces. We relate these spaces to the Teichmuller spaces of W-gravity. We show how this provides a covariant description of W-gravity and naturally leads to a Polyakov path integral prescription for W-strings. (Talk presented at the International Colloquium on Modern Quantum Field Theory II at the Tata Institute, Bombay during Jan. 5-11, 1994, to appear in the proceedings)