Isomonodromic tau-function of Hurwitz Frobenius manifolds and its applications

Details Isomonodromic tau-function of Hurwitz Frobenius manifolds and its applications Isomonodromic tau-function of Hurwitz Frobenius manifolds and its applications

2003-10-07

arxiv.org/abs/math-ph/0310008v2

Physics

Mathematical Physics

The direct proof of variational formulas on branched coverings is added. The title is modified due to observed coincidence of

Scientific paper

In this work we find the isomonodromic (Jimbo-Miwa) tau-function corresponding to Frobenius manifold structures on Hurwitz spaces. We discuss several applications of this result. First, we get an explicit expression for the G-function (solution of Getzler's equation) of the Hurwitz Frobenius manifolds. Second, in terms of this tau-function we compute the genus one correction to the free energy of hermitian two-matrix model. Third, we find the Jimbo-Miwa tau-function of an arbitrary Riemann-Hilbert problem with quasi-permutation monodromy matrices. Finally, we get a new expression (analog of genus one Ray-Singer formula) for the determinant of Laplace operator in the Poincar\'e metric on Riemann surfaces of an arbitrary genus.

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