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

TL;DR

This paper shows that gravitational descendants in topological Landau-Ginzburg theories coupled to gravity can be built solely from matter fields, revealing connections with K.Saito's higher residue pairing and providing explicit correlation function calculations.

Contribution

It introduces a method to construct gravitational descendants from matter fields alone and clarifies their relation to higher residue pairings, with corrected computations of correlation functions.

Findings

Descendants constructed from matter fields are connected to K.Saito's pairing.

Contact terms are essential for correcting naive correlation function calculations.

Explicit k-point correlation functions on a sphere are computed.

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.