Descendants constructed from matter fields in topological Landau-Ginzburg theories coupled to topological gravity

Abstract

It is argued that gravitational descendants in Landau-Ginsburg theory coupled to topological gravity can be constructed from the matter fields only. For example, $\sigma_1 (\Phi) = V'\int \Phi$. This descendants turn out to be connected with K.Saito higher residue pairing. Naive computaitions are corrected with the help of the contact term, the form of this term is found. k-point correlation functions on a sphere are calculated.