CONFORMAL MATRIX MODELS AS AN ALTERNATIVE TO CONVENTIONAL MULTIMATRIXMODELS

We introduce conformal multi-matrix models (CMMs) as an alternative to conventional multi-matrix model description of two-dimensional gravit y interacting with c < 1 matter. We define CMMs as solutions to (discr ete) extended Virasoro constraints. We argue that the so defined alter natives of multi-matrix models represent the same universality classes in the continuum limit, while at the discrete level they provide expl icit solutions to the multi-component KP-hierarchy and by definition s atisfy the discrete W-constraints. We prove that discrete CMMs coincid e with the (p, q)-series of 2d gravity models in a well-defined contin uum limit, thus demonstrating that they provided a proper generalizati on of the hermitian one-matrix model.