Structures of K.Saito theory of primitive form in topological theories coupled to topological gravity

Abstract

Structure of topological theory coupled to topological gravity is studied on a typical example — Landau-Ginzburg theory. It is shown that all main ingredients of K.Saito theory of primitive form are implied in such gravity theory. Filtration, that he considers turns out to be filtration by degrees of Morita-Mamford classes, and can be considered as a filtration of equivariant cohomologies (equivariance with respect to rotation of local coordinate). Higher residue pairing are nothing by pairing in equivariant cohomologies induced by integration over C ^d. Section is the kernel of a contact term map. Axioms on goods sections follow from the symmetry of n-point correlation functions on genus zero.

This work was partially supported by Grant 93-02-14365 of the Russian foundation of fundamental research.