A new spin on Hurwitz theory and ELSV via theta characteristics
Abstract 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 Kähler surfaces and to representation theory of the Sergeev group, and are generated by BKP tau-functions. We use the latter interpretation to give polynomiality properties of these numbers and we derive a spectral curve which we conjecture computes spin Hurwitz numbers via a new type of topological recursion. We prove that this conjectural topological recursion is equivalent to an ELSV-type formula, expressing spin Hurwitz numbers in terms of the Chiodo class twisted by the 2-spin Witten class.
Authors
- Reinier Kramer (ORCID: https://orcid.org/0000-0001-9649-9501)
- Danilo Lewański (ORCID: https://orcid.org/0000-0002-9706-008X)
- Alessandro Giacchetto (ORCID: https://orcid.org/0000-0001-8415-5066)
Institutions
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Laboratoire de Physique Théorique (FR)
- Max Planck Institute for Mathematics (DE)
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca (IT)
- Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (IT)
- Institut de Physique Théorique (FR)
- Institut des Hautes Études Scientifiques (FR)
Publication Details
- Journal
- Selecta Mathematica
- Published
- 2025-09-24
- DOI
- https://doi.org/10.1007/s00029-025-01077-y
- Citations
- 6
- Primary Topic
- Nonlinear Waves and Solitons
- Type
- article
- Field-Weighted Citation Impact
- 1.32
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Eidgenössische Technische Hochschule Zürich
- Max-Planck-Gesellschaft
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni