THE STRING THEORY APPROACH TO GENERALIZED 2D YANG-MILLS THEORY

We calculate the partition function of the SU(N) (and U(N)) generalize d YM(2) theory defined on an arbitrary Riemann surface. The result whi ch is expressed as a sum over irreducible representations generalizes the Rusakov formula for ordinary YM(2) theory. A diagrammatic expansio n of the formula enables us to derive a Gross-Taylor-like stringy desc ription of the model. A sum of 2D string maps is shown to reproduce th e gauge theory results. Maps with branch points of degree higher than one, as well as ''microscopic surfaces'', play an important role in th e sum. We discuss the underlying string theory.