Chiral Rings in Topological (W-)Gravity

TL;DR

This paper reviews the superconformal structure of 2D matter coupled to gravity, explores topological strings, and introduces new theories based on W-gravity, linking Liouville theory and matrix models.

Contribution

It provides a comprehensive review of superconformal properties in topological gravity and introduces an infinite class of new W-gravity theories.

Findings

Clarified the link between Liouville theory and matrix models.

Constructed new theories based on W-gravity.

Enhanced understanding of superconformal structures in 2D gravity.

Abstract

Talk given at the 26th Workshop: ``From Superstrings to Supergravity", Erice - Sicily, 5-12 December 1992. We review the superconformal properties of 2d matter coupled to gravity, and extensions thereof. Focusing on topological strings, we recall how the superconformal structure helps to provide a direct link between Liouville theory coupled to matter, and matrix models. We also construct an infinite class of new theories based on $W$-gravity.