KP hierarchy for Hurwitz-type cohomological field theories

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.

Keywords

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

2010 Mathematics Subject Classification

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

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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