Isomonodromic tau-function of Hurwitz Frobenius manifolds and its applications

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dc.creatorKokotov, A.
dc.creatorKorotkin, D.
dc.date2003-10-07
dc.date2005-03-23
dc.date.accessioned2026-07-07T04:30:36Z
dc.date.available2026-07-07T04:30:36Z
dc.descriptionIn 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 Poincaré metric on Riemann surfaces of an arbitrary genus.
dc.descriptionThe direct proof of variational formulas on branched coverings is added. The title is modified due to observed coincidence of isomonodromic tau-function of Hurwitz Frobenius manifolds with Bergman tau-function on Hurwitz spaces introduced by the authors
dc.identifierhttps://arxiv.org/abs/math-ph/0310008
dc.identifierhttp://arxiv.org/abs/math-ph/0310008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57522
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subject53D45, 34M55
dc.titleIsomonodromic tau-function of Hurwitz Frobenius manifolds and its applications
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