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arXiv · 2412.17502

$\mathfrak{b}$-Hurwitz numbers from refined topological recursion

Nitin Kumar Chidambaram·Maciej Dołęga·Kento Osuga
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Abstract

We prove that single $G$-weighted $\mathfrak{b}$-Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights $G$. Consequently, the $\mathfrak{b}$-Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of $\mathfrak{b}$-monotone Hurwitz numbers, and the enumeration of maps and bipartite maps (with internal faces) on non-oriented surfaces. As an application, we prove that the correlators of the Gaussian, Jacobi and Laguerre $\beta$-ensembles are computed by refined topological recursion.

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Nitin Kumar Chidambaram, Maciej Dołęga, Kento Osuga. 2024-12-23. $\mathfrak{b}$-Hurwitz numbers from refined topological recursion. https://doi.org/10.1007/s00208-026-03418-4

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