Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces

Details Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces

1997-03-26

arxiv.org/abs/hep-th/9703189v1

Commun.Math.Phys. 191 (1998) 283-298

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 2 figures, TeX, harvmac.tex, epsf.tex, TeX "big"

Scientific paper

10.1007/s002200050269

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

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