Blobbed topological recursion and KP integrability

TL;DR

This paper extends blobbed topological recursion to generalized settings, demonstrating KP integrability for a broader class of differentials, including non-perturbative cases, thereby unifying and strengthening previous results.

Contribution

It introduces a generalized framework for blobbed topological recursion and proves KP integrability for these generalized differentials, including non-perturbative cases.

Findings

KP integrability holds for blobbed topological recursion with KP-integrable blobs

The framework unifies perturbative and non-perturbative differentials

Provides a new proof of KP integrability conjecture by Borot--Eynard

Abstract

We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP integrability of the differentials of blobbed topological recursion for the input data that include KP-integrable blobs. This result generalizes, unifies, and gives a new proof of the KP integrability of nonperturbative differentials conjectured by Borot--Eynard and recently proved by the authors.