Relations between the correlators of the topological sigma-model coupled to gravity

Abstract

We prove a new recursive relation between the correlators $<{\tau }_{d_1}{\gamma }_1...{\tau }_{d_n}{\gamma }_n{>}_{g,\beta }$, which together with known relations allows one to express all of them through the full system of Gromov-Witten invariants in the sense of Kontsevich-Manin and the intersection indices of tautological classes on ${\bar{M}}_{g,n}$, effectively calculable in view of earlier results due to Mumford, Kontsevich, Getzler, and Faber. This relation shows that a linear change of coordinates of the big phase space transforms the potential with gravitational descendants to another function defined completely in terms of the Gromov-Witten correspondence and the intersection theory on $V^n\times {\bar{M}}_{g,n}$. We then extend the formalism of gravitational descendants from quantum cohomology to more general Frobenius manifolds and Cohomological Field Theories.

AMS-Tex, 13 pages, no figures

References in corpus (2)

• Quantum Cohomology and Virasoro Algebra
• Topological recursion relations in genus 2

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