Year: 2026
Type: preprint
Abstract: In this paper we study the Borel summability and quantum modularity of the free energy computed by refined topological recursion on the Weber-type refined spectral curve. On the one hand, we verify expected properties, namely, Stokes rays come in a pair and the Borel-Laplace sum of the free energy coincides with the Barnes double gamma function. Somewhat unexpectedly, on the other hand, we prove that the generating function of the Stokes constants along each ray is a Jacobi quantum modular function. Our proof suggests that quantum modularity may be a general feature of refined topological recursion, applicable beyond the Weber-type refined spectral curve.
Source: arXiv (Cornell University)
Authors: Fantini, Veronica, Osuga, Kento
Institutions: Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214008680
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