KP hierarchy for Hurwitz-type cohomological field theories

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.

arXiv comment21 pages. v2: added report number to metadata, file unchanged. v3: corrected errors, added example, updated references. v4: clarified relation between triple Hodge integrals and Bychkov-Dunin-Barkowski-Kazarian-Shadrin's work