On the Landau-Ginzburg Realization of Topological Gravities

TL;DR

This paper explores the connection between multi-field topological Landau-Ginzburg models and $W$-gravity, revealing a richer spectrum and constructing the gravitational chiral ring using LG polynomials.

Contribution

It introduces a novel approach to understanding $W$-gravity through equivariant cohomology of LG models and constructs the gravitational chiral ring.

Findings

The spectrum of these theories is richer than previously thought.

The gravitational chiral ring can be constructed from LG polynomials.

Insights into the BRST operator for non-linear topological $W$-gravity.

Abstract

We study the equivariant cohomology of a class of multi-field topological LG models, and find that such systems carry intrinsic information about $W$-gravity. As a result, we can construct the gravitational chiral ring in terms of LG polynomials. We find, in particular, that the spectrum of such theories seems to be richer than so far expected. We also briefly discuss the BRST operator for non-linear topological $W$-gravity.