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

被引：9

作者：

Bertola, M. ^{[1
,4
]}

Marchal, O. ^{[2
,3
,4
]}

机构：

[1] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

[2] CEA, Inst Phys Theor, IPhT, F-91191 Gif Sur Yvette, France

[3] CNRS, URA 2306, F-91191 Gif Sur Yvette, France

[4] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2009年 / 50卷 / 01期

关键词：

integration; matrix algebra; polynomials; RIEMANN-HILBERT PROBLEM; ORDINARY DIFFERENTIAL-EQUATIONS; BIORTHOGONAL POLYNOMIALS; MATRIX MODELS; EIGENVALUE CORRELATIONS; RATIONAL COEFFICIENTS; DETERMINANTS; DEFORMATION; DUALITY; GRAVITY;

D O I：

10.1063/1.3054865

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 that of Jimbo [ "Monodromy preserving deformation of linear ordinary differential equations with rational coefficients," Physica D 2, 306 (1981)]. In order to achieve the generalization we need to define a notion of tau function for isomonodromic systems where the adregularity of the leading coefficient is not a necessary requirement.

引用

页数：17

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