PreprintCC BY 4.0arXiv
Haagerup conformal field theory at central charge eight
Abstract
We construct a chiral algebra U of central charge eight inside the lattice vertex operator algebra VE6⊕ A2. It is generated by two commuting affine sl2 current algebras at levels $1$ and $39$, the stress tensor of the lattice theory, and a single weight-two field built from three lattice exponentials. We announce that U is strongly rational and completely unitary, and that Rep(U) is equivalent, as a unitary ribbon category, to the Drinfeld center Z(ℋ3) of the Haagerup fusion category ℋ3. Its characters are the γ=0 Evans--Gannon vector. From U we obtain a diagonal full CFT, and also a holomorphic E8 extension on which ℋ3 acts by topological defects.
Related
- Haagerup symmetries of the E8 theory and conformal nets at central charge eight
- Haagerup-Izumi modular data from hyperbolic words: S-fold TQFTs, central charge, torsion and the Bethe vacua
- Haagerup vertex operator algebras at central charge eight
- Conformal field theory from automorphic forms on a quantum group
- The modular energy range of an interval in chiral conformal field theory
BibTeX
@misc{huang2026haagerup,
title = {{Haagerup conformal field theory at central charge eight}},
author = {Tzu-Chen Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14441},
eprint = {2610.14441},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14441},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Haagerup conformal field theory at central charge eight
AU - Tzu-Chen Huang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.14441
UR - https://arxiv.org/abs/2610.14441
AB - We construct a chiral algebra U of central charge eight inside the lattice vertex operator algebra V_E_6⊕ A_2. It is generated by two commuting affine sl_2 current algebras at levels $1$ and $39$, the stress tensor of the lattice theory, and a single weight-two field built from three lattice exponentials. We announce that U is strongly rational and completely unitary, and that Rep(U) is equivalent, as a unitary ribbon category, to the Drinfeld center Z(ℋ_3) of the Haagerup fusion category ℋ_3. Its characters are the γ=0 Evans--Gannon vector. From U we obtain a diagonal full CFT, and also a holomorphic E_8 extension on which ℋ_3 acts by topological defects.
ER -