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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.05510
- arXiv:
- arXiv:2107.05510
- Bibcode:
- 2021arXiv210705510K
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- 37K10;
- 14N35;
- 81R10;
- 14N10;
- 05A15
- E-Print:
- 21 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