Any topological recursion on a rational spectral curve is KP integrable

TL;DR

This paper demonstrates that topological recursion on a genus zero spectral curve yields correlation differentials that are KP integrable, linking it to integrable systems and enumerative geometry.

Contribution

It establishes KP integrability for correlation differentials from topological recursion on genus zero spectral curves, extending the understanding of integrable structures in enumerative geometry.

Findings

Correlation differentials are KP integrable for genus zero spectral curves.

Partition functions related to ELSV-type formulas are KP integrable.

Provides a new connection between topological recursion and KP integrability.

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 $r$-th roots of the twisted powers of the log canonical bundles.