# Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type

@inproceedings{Bychkov2020TopologicalRF, title={Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type}, author={Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Viktorovich Shadrin}, year={2020} }

We study the n-point differentials corresponding to Kadomtsev–Petviashvili tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their ~-deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov…

## 13 Citations

Topological recursion for Orlov-Scherbin tau functions, and constellations with internal faces

- Mathematics
- 2022

We study the correlators W g,n arising from Orlov–Sherbin 2-Toda tau functions with rational content-weight G ( z ) , at arbitrary values of the two sets of time parameters. Combinatorially, they…

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

- 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…

Enumeration of non-oriented maps via integrability

- Mathematics
- 2021

ABSTRACT. In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrence…

Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy

- MathematicsLetters in Mathematical Physics
- 2021

We consider the Dubrovin–Frobenius manifold of rank 2 whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the…

Symplectic duality for topological recursion

- Mathematics
- 2022

. We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the…

A new spin on Hurwitz theory and ELSV via theta characteristics

- Mathematics
- 2021

We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of…

KP hierarchy for Hurwitz-type cohomological field theories

- Mathematics
- 2021

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…

Integrality in the Matching-Jack conjecture and the Farahat-Higman algebra

- Mathematics
- 2021

. Using Jack polynomials, Goulden and Jackson have introduced a b -deformation τ b of the generating series of bipartite maps. The Matching-Jack conjecture suggests that the coefﬁcients c λµ , ν of…

On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator

- Mathematics
- 2022

Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data (Σ, x, y, B). We give a functional relation between the correlators of genus g = 0…

Explicit closed algebraic formulas for Orlov–Scherbin n-point functions

- Mathematics, PhysicsJournal de l’École polytechnique — Mathématiques
- 2022

—We derive a new explicit formula in terms of sums over graphs for the n-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev–Petviashvili tau…

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