The partition function of the two-matrix model as an isomonodromic τ function
Abstract
We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic τ function in a sense that generalizes that of Jimbo et al. [ "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 τ function for isomonodromic systems where the adregularity of the leading coefficient is not a necessary requirement.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- January 2009
- DOI:
- 10.1063/1.3054865
- arXiv:
- arXiv:0809.1598
- Bibcode:
- 2009JMP....50a3529B
- Keywords:
-
- 02.10.Yn;
- 02.10.De;
- 02.30.Cj;
- Matrix theory;
- Algebraic structures and number theory;
- Measure and integration;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 22 pages, 1 figure