On the Landau-Ginzburg realization of topological gravities

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.