Two-matrix model with semiclassical potentials and extended Whitham hierarchy

Abstract

We consider the two-matrix model with potentials whose derivative are arbitrary rational function of fixed pole structure and the support of the spectra of the matrices are union of intervals (hard-edges). We derive an explicit formula for the planar limit of the free energy and we derive a calculus which allows to compute derivatives of arbitrarily high order by extending classical Rauch's variational formulae. The four-points correlation functions are explicitly worked out. The formalism extends naturally to the computation of residue formulae for the tau function of the so-called universal Whitham hierarchy studied mainly by I. Krichever: our setting extends that moduli space in that there are certain extra data.

32 pages, one figure

References in corpus (1)

• Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

Cited by in corpus (2)

• Free energy topological expansion for the 2-matrix model
• Topological expansion of the chain of matrices