COMPLEX MATRIX MODELS AND STATISTICS OF BRANCHED-COVERINGS OF 2D SURFACES

We present a complex matrix gauge model defined on an arbitrary two-di mensional orientable lattice. We rewrite the model's partition functio n in terms of a sum over representations of the group U(N). The model solves the general combinatorial problem of counting branched covers o f orientable Riemann surfaces with any given, fixed branch point struc ture, We then define an appropriate continuum limit allowing the branc h points to freely float over the surface, The simplest such limit rep roduces two-dimensional chiral U(N) Yang-Mills theory and its string d escription due to Gross and Taylor.