THE ROLE OF THE CONTACT ALGEBRA IN MULTIMATRIX MODELS

In this paper we investigate the implications of the topological nature of the (1, q) matrix models. We show that the algebraic structure is enough to derive the correlation functions of pure gravity. A straightforward generalization for several primaries is presented. We further find that the recursion relations in the multimatrix models may be derived from the contact algebra alone. We show that the contact algebra, using the ghost number assignment derived from the KdV hierarchy, is consistent only for contacts with the puncture operator and its descendents. We discuss the role of the contact algebra and its consistency in general.