THE 2-MATRIX MODEL AT FINITE N AND THE 2D TODA HIERARCHY

Abstract

We give a rigorous proof that the partition function of the standard hermitian two-matrix model at finite N is a tau-function of the 2d Toda hierarchy. The proof is based on the establishment of a characteristic bilinear relation for the associated Baker-Akhiezer functions, which we have explicitly constructed in terms of the orthogonal polynomials of the matrix model.