On the continuum limit of the conformal matrix models

The double scaling limit of a new class of the multi-matrix models proposed in [1], which possess the W-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the paper [2] is proposed, the corresponding partition functions being compared. All calculations are demonstrated in full in the first non-trivial case of W⁽³⁾-constraints.This paper was supported in part by NSF grant PHY88-57200.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 317–340, May, 1993.