2-DIMENSIONAL CHIRAL MATRIX MODELS AND STRING THEORIES

We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, dis cretized, two-dimensional manifold. We interpret the models as string theories characterized by a set of coupling constants associated to wo rldsheet ramification points of various orders. Our approach is closel y related to, but simpler than, the string theory describing two-dimen sional Yang-Mills theory. Using recently developed character expansion methods we exactly solve the models for target space lattices of arbi trary internal connectivity and topology.