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The Haagerup VOA at Central Charge Eight

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.CT — Category Theory

Contributed by Andrew Riesen ↗

Version 1 / Oct 10, 2026 / CC BY 4.0

Abstract

We give an explicit construction of a vertex operator algebra UU of central charge eight inside VE6⊕A2V_{E_6\oplus A_2}, and prove the ribbon equivalence $\Rep(U)\simeq Z(\HH_3)$, where $\HH_3$ is a Haagerup fusion category. The algebra is generated as a vertex algebra by six affine generators and three specified weight-two vectors. The argument combines exact lattice-vector calculations with an all-weight strong-generation induction, a finite presentation and semisimple descent for a full corner of Zhu's algebra, and the actual multiplication of two holomorphic E8E_8 extensions. The categorical identification uses splitting maps and a comparison with the Evans--Gannon reconstruction, not modular data alone.

Provenance statement

Generative AI was used under the author’s direction to develop the candidate construction and initial proof arguments and to generate substantial portions of the manuscript text and code. The author set the research objective, guided the mathematical strategy, and has substantially refined the arguments, notation, and exposition. The author understands the high-level arguments. However, the detailed computations, the correctness and adequacy of their verification procedures, and whether their outputs establish all the required mathematical conclusions have not yet been independently verified by the author. The claimed results therefore remain provisional. This is a work in progress that the author is actively developing into a paper whose arguments and computations can be checked by human mathematicians. Community feedback is welcomed on mathematical correctness, presentation, appropriate attribution, and historical accuracy.

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Version history

  1. v1Submitted by Andrew RiesenInitial depositCurrentOct 09, 2026