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

Abstract

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 sums which are given by Orlov's hypergeometric solutions of the 2-component BKP hierarchy. We derive the closed algebraic formulas for the correlation functions associated with these tau-functions, and under reasonable analytical assumptions we prove the loop equations (the blobbed topological recursion). Finally, we prove a version of topological recursion for the spin Hurwitz numbers with the spin completed cycles (a generalized version of the Giacchetto--Kramer--Lewański conjecture).

arXiv comment31 pages, minor corrections

References in corpus (11)

• Blobbed topological recursion: properties and applications
• The Adler-Shiota-van Moerbeke formula for the BKP hierarchy
• Spin Hurwitz numbers and topological quantum field theory
• Weighted Hurwitz numbers and topological recursion: an overview
• Generating functions for weighted Hurwitz numbers
• Weighted Hurwitz numbers and topological recursion
• Cut-and-join structure and integrability for spin Hurwitz numbers
• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• Explicit closed algebraic formulas for Orlov-Scherbin $n$-point functions
• Generalized Brézin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy
• Special cases of the orbifold version of Zvonkine's $r$-ELSV formula

Cited by in corpus (4)

• Connected $(n,m)$-Point Functions of Diagonal $2$-BKP Tau-Functions, and Spin Double Hurwitz Numbers
• A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
• Blobbed topological recursion and KP integrability
• Any topological recursion on a rational spectral curve is KP integrable