MULTIMATRIX MODELS AND THE KP HIERARCHY

We analyze the critical points of multi-matrix models. In particular we find the critical points of highest multi-criticality of the symmetric two-matrix model with an even potential. We solve the model on the sphere and show that these critical points correspond to the (p, q) minimal models with p + q = odd. Based on this experience we give a formulation of minimal models coupled to quantum gravity, in terms of differential operators, that makes the w1 + infinity constraints very transparent. This formulation provides a natural setting to study many issues, such as flows changing both p and q.