{Descendants constructed from matter field in Landau--Ginzburg theories coupled to

A. S. Losev

Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 2, pp. 307-316

Résumé

It is argued that gravitational descendants in the theory of topological gravity coupled to topological Landau–Ginzburg theory(not necessarily conformal) can be constructed from matter fields alone (without metric fields and \hbox {ghosts}). In this sense topological gravity is “induced”. We discuss the mechanism of this effect (that turns out to be connected with K. Saito's higher residue pairing: $K^i(\sigma _i (\Phi _1), \Phi _2)=K^0(\Phi _1, \Phi _2)$),and demonstrate how it works in a simplest nontrivial example: correlator on a sphere with four marked points. We also discuss some results on $k$-point correlators on a sphere. From the idea of “induced” topological gravity it follows that the theory of “pure” topological gravity (without topological matter) is equivalent to the “trivial” Landau–Ginzburg theory (with quadratic superpotential).