The partition function of the two-matrix model as an isomonodromic tau-function

Abstract

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. 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.

22 pages, 1 figure

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• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• Planar Orthogonal Polynomials As Type II Multiple Orthogonal Polynomials
• Painlev'e 2 equation with arbitrary monodromy parameter, topological recursion and determinantal formulas
• Painlevé equations, topological type property and reconstruction by the topological recursion
• From the quantum geometry of Fuchsian systems to conformal blocks of W-algebras