Communications in Number Theory and Physics

Volume 17 (2023)

Number 2

KP hierarchy for Hurwitz-type cohomological field theories

Pages: 249 – 291



Reinier Kramer (University of Alberta, Edmonton, AB, Canada)


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 DOSS correspondence between topological recursion and cohomological field theories. As a particular case, we recover the result of Alexandrov of KP integrability for triple Hodge integrals with a Calabi–Yau condition.


Hurwitz theory, integrable hierarchies, cohomological field theories, topological recursion

2010 Mathematics Subject Classification

Primary 14H10, 37K10. Secondary 14H70, 14N35, 37K20, 37K25.

Research conducted for this paper is supported by the Netherlands Organization for Scientific Research, the Max-Planck-Gesellschaft, the Natural Sciences and Engineering Research Council of Canada, and the Pacific Institute for the Mathematical Sciences (PIMS).

Received 18 January 2022

Accepted 27 February 2023

Published 4 May 2023