Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models

Abstract

We introduce {\it conformal multi-matrix models} (CMM) as an alternative to conventional multi-matrix model description of two-dimensional gravity interacting with $c<1$ matter. We define CMM as solutions to (discrete) extended Virasoro constraints. We argue that the so defined alternatives of multi-matrix models represent the same universality classes in 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 CMM coincide with the $(p,q)$-series of 2d gravity models in a {\it well}-{\it defined} continuum limit, thus demonstrating that they provide a proper generalization of Hermitian one-matrix model.

35 pages, preprint FIAN/TD-9/92 & ITEP-M-4/92

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