PreprintCC BY 4.0arXiv
Cyclic Haagerup-Izumi fusion categories at every odd order
Abstract
We construct a complex spherical fusion category with cyclic Haagerup-Izumi fusion rules for every odd n >= 3, and deduce pseudo-unitary existence. The proof has four parts: explicit real coefficients and their quadratic identities; a contour calculation for a range of cubic Fourier coefficients; algebraic completion of all cubics; and categorical reconstruction. Matrix inversion supplies reflection, and an extension of the dimension-field automorphism supplies the positive-dimensional category.
Related
- On Haagerup-Izumi fusion categories
- A vertex operator algebra for the S-fold realisation of a non-unitary Haagerup--Izumi modular fusion category
- Vertex operator algebra realizations of untwisted Haagerup--Izumi centers
- Haagerup-Izumi modular data from hyperbolic words: S-fold TQFTs, central charge, torsion and the Bethe vacua
- A diagrammatic presentation for every pivotal pointed fusion category
BibTeX
@misc{huang2026cyclic,
title = {{Cyclic Haagerup-Izumi fusion categories at every odd order}},
author = {Tzu-Chen Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15986},
eprint = {2609.15986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15986},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cyclic Haagerup-Izumi fusion categories at every odd order
AU - Tzu-Chen Huang
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15986
UR - https://arxiv.org/abs/2609.15986
AB - We construct a complex spherical fusion category with cyclic Haagerup-Izumi fusion rules for every odd n >= 3, and deduce pseudo-unitary existence. The proof has four parts: explicit real coefficients and their quadratic identities; a contour calculation for a range of cubic Fourier coefficients; algebraic completion of all cubics; and categorical reconstruction. Matrix inversion supplies reflection, and an extension of the dimension-field automorphism supplies the positive-dimensional category.
ER -