9 research outputs found

    Genus one contribution to free energy in hermitian two-matrix model

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    We compute an the genus 1 correction to free energy of Hermitian two-matrix model in terms of theta-functions associated to spectral curve arising in large N limit. We discuss the relationship of this expression to isomonodromic tau-function, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian in a singular metric over spectral curve.Comment: 25 pages, detailed version of hep-th/040116

    1/N21/N^2 correction to free energy in hermitian two-matrix model

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    Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for F1F^1 in hermitian one-matrix model. We discuss the relationship between F1F^1, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian over spectral curve

    Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities

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    In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy) problem corresponding to Frobenius structures on Hurwitz spaces. We find a solution to this Riemann-Hilbert problem in terms of integrals of certain meromorphic differentials over a basis of an appropriate relative homology space, study the corresponding monodromy group and compute the monodromy matrices explicitly for various special cases.Comment: final versio

    Matrix models, complex geometry, and integrable systems: II^*

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