Partition functions for Matrix Models and Isomonodromic Tau functions
نویسندگان
چکیده
For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2×2 polynomial differential systems satisfied by the associated orthogonal polynomials is derived.
منابع مشابه
Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such measures. These are shown to preserve the generalized monodromy of the associated rank-2 rational covariant derivative operators. The corresponding matrix m...
متن کاملMoment determinants as isomonodromic tau functions
We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann–Hilbert problem asso...
متن کاملThe partition function of the two-matrix model as an isomonodromic tau-function
We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno’s [20]. In order to achieve the generalization we need to define a notion of tau-function for isomonodromic systems where the ad–regularity of the leading coefficient is not a necessary requirement.
متن کاملIsomonodromic deformations in genus zero and one: algebrogeometric solutions and Schlesinger transformations
Here we review some recent developments in the theory of isomonodromic deformations on Riemann sphere and elliptic curve. For both cases we show how to derive Schlesinger transformations together with their action on tau-function, and construct classes of solutions in terms of multi-dimensional theta-functions. The theory of isomonodromic deformations of ordinary matrix differential equations o...
متن کاملIsomonodromic tau-functions from Liouville conformal blocks
The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c = 1. This implies a similar representation for the isomonodromic tau-function. In the case n = 4 we thereby g...
متن کامل