Any topological recursion on a rational spectral curve is KP integrable
Mathematical Physics
2026-05-19 v2 High Energy Physics - Theory
Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We prove that for any initial data on a genus zero spectral curve the corresponding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the -th roots of the twisted powers of the log canonical bundles.
Cite
@article{arxiv.2406.07391,
title = {Any topological recursion on a rational spectral curve is KP integrable},
author = {Alexander Alexandrov and Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Shadrin},
journal= {arXiv preprint arXiv:2406.07391},
year = {2026}
}
Comments
16 pages; several corrections and clarifications; a complete proof of Theorem A.1 added