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arXiv · 2002.00466

Hurwitz numbers from matrix integrals over Gaussian measure

Sergei M. Natanzon·Aleksandr Yu. Orlov
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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.

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Sergei M. Natanzon, Aleksandr Yu. Orlov. 2020-02-02. Hurwitz numbers from matrix integrals over Gaussian measure. https://arxiv.org/abs/2002.00466

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