Year: 2025
Type: article
Abstract: Hurwitz numbers enumerate branched morphisms between Riemann surfaces. For a fixed elliptic target, Hurwitz numbers are intimately related to mirror symmetry following work of Dijkgraaf. In recent work of Chapuy and Dołęga, a new variant of Hurwitz numbers with fixed genus 0 target was introduced that includes maps between non-orientable surfaces. These numbers are called b -Hurwitz numbers and are polynomials in a parameter b which measures the non-orientability of the involved maps. An interpretation in terms of factorisations of b -Hurwitz numbers for b=1 , so-called twisted Hurwitz numbers, was found in work of Burman and Fesler. In previous work, the authors derived a tropical geometry interpretation of these numbers. In this paper, we introduce a natural generalisation of twisted Hurwitz numbers with elliptic targets within the framework of symmetric groups. We derive a tropical interpretation of these invariants, relate them to Feynman integrals and derive an expression as a matrix element of an operator in the bosonic Fock space.
Source: Documenta Mathematica
DOI: 10.4171/dm/1041
Authors: Marvin Anas Hahn, Hannah Markwig
Institutions: Trinity College Dublin, University of Tübingen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4414409870
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