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

@article{Kostov1998ComplexMM,
  title={Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces
},
  author={Ivan Kostov and Matthias Staudacher and Thomas Wynter},
  journal={Communications in Mathematical Physics},
  year={1998},
  volume={191},
  pages={283-298}
}
Abstract: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… 
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