Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation

Abstract

We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov - Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.

53 pages, Latex, two references added, some typos corrected, version to appear in Commun. Math. Phys

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