The String Theory Approach to Generalized 2D Yang-Mills Theory

Abstract

We calculate the partition function of the $SU(N)$ ( and $U(N)$) generalized $Y{M}_2$ theory defined on an arbitrary Riemann surface. The result which is expressed as a sum over irreducible representations generalizes the Rusakov formula for ordinary YM_2 theory. A diagrammatic expansion of the formula enables us to derive a Gross-Taylor like stringy description of the model. A sum of 2D string maps is shown to reproduce the gauge theory results. Maps with branch points of degree higher than one, as well as ``microscopic surfaces'' play an important role in the sum. We discuss the underlying string theory.

TAUP-2182-94, 53 pages of LaTeX and 5 uuencoded eps figures

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