English

Hurwitz numbers from matrix integrals over Gaussian measure

Mathematical Physics 2020-03-10 v3 math.MP

Abstract

We explain how Gaussian integrals over ensemble of complex matrices with source matrices generate Hurwitz numbers of the most general type, namely, Hurwitz numbers with arbitrary orientable or non-orientable base surface and arbitrary profiles at branch points. We use the Feynman diagram approach. The connections with topological theories and also with certain classical and quantum integrable theories in particular with Witten's description of two-dimensional gauge theory are shown.

Keywords

Cite

@article{arxiv.2002.00466,
  title  = {Hurwitz numbers from matrix integrals over Gaussian measure},
  author = {Sergei M. Natanzon and Aleksandr Yu. Orlov},
  journal= {arXiv preprint arXiv:2002.00466},
  year   = {2020}
}

Comments

29 pages, 4 figures, misprints removed

R2 v1 2026-06-23T13:28:22.002Z