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

References in corpus (13)

• Integrable Hierarchies and Dispersionless Limit
• Towards an enumerative geometry of the moduli space of twisted curves and r-th roots
• Identification of the Givental formula with the spectral curve topological recursion procedure
• Geometry of Spectral Curves and All Order Dispersive Integrable System
• Equivalence of ELSV and Bouchard-Mariño conjectures for $r$-spin Hurwitz numbers
• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• Explicit closed algebraic formulas for Orlov-Scherbin $n$-point functions
• Loop equations and a proof of Zvonkine's $qr$-ELSV formula
• Chiodo formulas for the r-th roots and topological recursion
• KP integrability through the $x-y$ swap relation
• Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
• A universal formula for the $x-y$ swap in topological recursion
• Enumeration of hypermaps and Hirota equations for extended rationally constrained KP