Any topological recursion on a rational spectral curve is 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.

16 pages; several corrections and clarifications; a complete proof of Theorem A.1 added