KP hierarchy for Hurwitz-type cohomological field theories

TL;DR

This paper extends KP hierarchy integrability results to a broad class of Hurwitz-type cohomological field theories, linking hypergeometric tau-functions, topological recursion, and Hodge integrals.

Contribution

It generalizes Kazarian's KP integrability result from single Hodge integrals to general Hurwitz-type cohomological field theories, using recent advances in topological recursion and tau-functions.

Findings

Establishes KP integrability for a wide class of Hurwitz-type theories.

Connects hypergeometric tau-functions with topological recursion.

Recovers Alexandrov's KP integrability for triple Hodge integrals.

Abstract

We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting problems or hypergeometric tau-functions. The proof uses recent results on the relations between hypergeometric tau-functions and topological recursion, as well as the Eynard-DOSS correspondence between topological recursion and cohomological field theories. In particular, we recover the result of Alexandrov of KP integrability for triple Hodge integrals with a Calabi-Yau condition.