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

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Title
Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
Author(s)
Alexander Alexandrov; Shadrin, Sergey
Publication Date
2023-04
Journal
SELECTA MATHEMATICA-NEW SERIES, v.29, no.2
Publisher
SPRINGER INT PUBL AG
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-Lewanski conjecture).
URI
https://pr.ibs.re.kr/handle/8788114/13072
DOI
10.1007/s00029-023-00834-1
ISSN
1022-1824
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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