KP integrability of non-perturbative differentials

Abstract

We prove the KP integrability of non-perturbative topological recursion, which can be considered as a formal $\hslash$-deformation of the Krichever construction of algebro-geometric solutions of the KP hierarchy. This property goes back to a 2011 conjecture of Borot and Eynard.

26 pages, v3: various corrections and clarifications, new Section 5 detailing the relation to Borot-Eynard formulations