Conformal matrix models as an alternative to conventional multi-matrix models

Abstract

We introduce conformal multi-matrix models (CMMs) as an alternative to conventional multi-matrix model description of two-dimensional gravity interacting with c < 1 matter. We define CMMs as solutions to (discrete) extended Virasoro constraints. We argue that the so defined alternatives of multi-matrix models represent the same universality classes in the continuum limit, while at the discrete level they provide explicit solutions to the multi-component KP-hierarchy and by definition satisfy the discrete W-constraints. We prove that discrete CMMs coincide with the ( p, q)-series of 2d gravity models in a well-defined continuum limit, thus demonstrating that they provided a proper generalization of the hermitian one-matrix model.