{
  "abstract": "For every odd integer $N\\geq3$, we construct an untwisted Haagerup--Izumi fusion category $\\mathcal H_N$ on the negative spherical branch and a simple, self-contragredient, regular, $C_2$-cofinite vertex operator algebra $E_N$ of central charge $-16N$, together with an equivalence of modular fusion categories: \\[ \\operatorname{Rep}(E_N)\\simeq Z(\\mathcal H_N). \\] The VOA $E_N$ is rational, has exactly $N^2+3$ irreducible modules, and is lower bounded and integer graded, with least conformal degree $-(N-1)/2$. The proof begins with a CFT-type cyclic Virasoro extension of central charge $-5N$, whose regularity we establish. Two categorical condensations recover $\\mathcal H_N$, and a finite extension by shifted lattice modules removes the auxiliary pointed factor. We identify the complete ribbon modular data of $Z(\\mathcal H_N)$ with $\\mathrm{MD}_{-}(\\mathbb Z/N;\\mathbb Z/(N^2+4),b\\mapsto b^2/(N^2+4))$ in the notation of Gannon--Schopieray--Yadav, for every odd $N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32928",
  "author_total": 2,
  "authors": [
    {
      "name": "David E. Evans"
    },
    {
      "name": "Andrew Riesen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97vnvkv60yexr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32928",
  "fulltext_url": null,
  "id": "97vnvkv60yexr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32928",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223668476",
  "pdf_url": "https://arxiv.org/pdf/2610.32928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97vnvkv60yexr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Vertex operator algebra realizations of untwisted Haagerup--Izumi centers",
  "title_text": "Vertex operator algebra realizations of untwisted Haagerup--Izumi centers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/97vnvkv60yexr",
  "venue": "arXiv",
  "versions": []
}