Genus one correction to free energy of Hermitian matrix models,
G-function of Hurwitz Frobenius manifolds and isomonodromic tau-function

Dmitri Korotkin

Abstract:

The theory of Frobenius manifolds and the theory of Hermitian matrix models are two different approaches to quantization of 2D topological field theories. Therefore, it is not very surprising that these theories turn out to be parallel in several aspects. In particular, in this talk we discuss similarities between the large N expansion in Hermitian two-matrix models and the genus expansion of the free energy of a class of Frobenius manifolds associated to Hurwitz spaces (spaces of meromorphic functions on Riemann surfaces). In both cases the computation of the higher order corrections to free energy is based on loop equations; in the subleading order the solution of the loop equations turns out to be very similar for the two models, and can be expressed via an appropriate isomonodromic tau function.

(Based on joint work with B.Eynard and A.Kokotov)