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

  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},
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… 
Branched coverings and interacting matrix strings in two dimensions
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  • Math. Phys. 177 (1996) 451; Comm. Math. Phys. 179 (1996) 235; Nucl. Phys. B 471
  • 1996
  • Phys. B 400 (1993) 161; D. Gross and W. Taylor, Nucl. Phys. B 400 (1993) 181; Nucl. Phys. B 403
  • 1993
  • B 437
  • 1995
  • Lett. B 97
  • 1980
Comm. Math. Phys. Nucl. Phys. B
  • Comm. Math. Phys. Nucl. Phys. B
  • 1996
Advances in Large N Group Theory and the Solution of Two-Dimensional R2
  • Gravity, hep-th/9601153,
  • 1995
Phys. B
  • Phys. B
  • 1995