Exact Solution of 1-matrix Model

Abstract

I review my new method for solving general 1-matrix models by expanding in $N^{-1}$ without taking a physical continuum limit. Using my method, each coefficient of the free energy in the genus expansion is exactly computable. One can include physical information in a function which is uniquely specified by the action of the model. My method gives completely the same result with the usual one if the physical fine tuning is done and the leading singular terms are extracted. I also calculate in the genus three case and confirm the validity of my method.