# KP hierarchy for Hurwitz-type cohomological field theories

@inproceedings{Kramer2021KPHF, title={KP hierarchy for Hurwitz-type cohomological field theories}, author={R. Kramer}, year={2021} }

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 taufunctions. 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… Expand

#### One Citation

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

- Mathematics, Physics
- 2021

In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi–Yau condition. For the tau-functions, which generate these integrals, we derive the complete families… Expand

#### References

SHOWING 1-10 OF 59 REFERENCES

KP hierarchy for Hodge integrals

- Mathematics
- 2008

Abstract Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and… Expand

BCOV theory via Givental group action on cohomological field theories

- Mathematics
- 2008

In a previous paper, Losev, the author, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of… Expand

The Structure of 2 D Semisimple Field Theories

- 2010

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the… Expand

Enumerative Geometry, Tau-Functions and Heisenberg–Virasoro Algebra

- Mathematics, Physics
- 2014

In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich–Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the… Expand

The structure of 2D semi-simple field theories

- Mathematics, Physics
- 2012

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the… Expand

Hurwitz numbers, matrix models and enumerative geometry

- Mathematics, Physics
- 2007

We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric… Expand

Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture

- Physics, Mathematics
- 2021

In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we construct the weighed… Expand

Dubrovin-Zhang hierarchy for the Hodge integrals

- Mathematics, Physics
- 2013

In this paper we prove that the generating series of the Hodge integrals over the moduli space of stable curves is a solution of a certain deformation of the KdV hierarchy. This hierarchy is… Expand

Hodge integrals, Hurwitz numbers, and Symmetric Groups

- Mathematics
- 2003

We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the… Expand

Multivariate hypergeometric functions as τ-functions of Toda lattice and Kadomtsev-Petviashvili equation

- Mathematics
- 2000

We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the… Expand