On geometry and matrix models

We point out two extensions of the relation between matrix models, topological strings and N = 1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi-Yau geometries that engineer N = 2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for Ar = I A DE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of A D E minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function. (C) 2002 Published by Elsevier Science B.V.