Isomonodromic tau-function of Hurwitz Frobenius manifolds and its applications
Kokotov, A. ; Korotkin, D.
arXiv, 0310008 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-10-07
Classification:  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  53D45, 34M55 
@article{0310008,
     author = {Kokotov, A. and Korotkin, D.},
     title = {Isomonodromic tau-function of Hurwitz Frobenius manifolds and its
  applications},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0310008}
}

Kokotov, A.; Korotkin, D. Isomonodromic tau-function of Hurwitz Frobenius manifolds and its
  applications. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0310008/