PreprintCC BY 4.0arXiv
The Haagerup VOA at c=8
Abstract
We announce an explicit construction of a unitary, strongly rational vertex operator algebra U of central charge $8$ inside VE6⊕ A2, with a ribbon equivalence Rep(U)≃ Z(ℋ3) realizing the Haagerup double. The vertex algebra is generated by six affine currents and three specified weight-two fields; its weight-one Lie algebra is sl2⊕sl2, at levels $1$ and $39$. We outline the argument, which combines exact lattice calculations, an all-weight strong-generation induction and C2-cofiniteness, semisimple descent for a full corner of Zhu's algebra, modular Galois symmetry, and holomorphic E8 extensions.
BibTeX
@misc{riesen2026haagerup,
title = {{The Haagerup VOA at $c=8$}},
author = {Andrew Riesen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13933},
eprint = {2610.13933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13933},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Haagerup VOA at c=8
AU - Andrew Riesen
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13933
UR - https://arxiv.org/abs/2610.13933
AB - We announce an explicit construction of a unitary, strongly rational vertex operator algebra U of central charge $8$ inside V_E_6⊕ A_2, with a ribbon equivalence Rep(U)≃ Z(ℋ_3) realizing the Haagerup double. The vertex algebra is generated by six affine currents and three specified weight-two fields; its weight-one Lie algebra is sl_2⊕sl_2, at levels $1$ and $39$. We outline the argument, which combines exact lattice calculations, an all-weight strong-generation induction and C_2-cofiniteness, semisimple descent for a full corner of Zhu's algebra, modular Galois symmetry, and holomorphic E_8 extensions.
ER -