# Any Topological Recursion on a Rational Spectral Curve is KP Integrable

## TL;DR

This paper shows that topological recursion on rational spectral curves leads to KP integrability, a key property in mathematical physics.

## Contribution

The paper proves that any topological recursion on a rational spectral curve is KP integrable.

## Key findings

- Correlation differentials from genus zero spectral curves are KP integrable.
- Partition functions from ELSV-type formulas are also KP integrable.

## 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.