{
  "abstract": "We introduce discrete $C^*$-Frobenius algebras as categorical data for constructing infinite-index extensions of Möbius covariant nets. The underlying representation is a countable direct sum of simple dualized modules, while the direct sum itself is not necessarily dualizable. Accordingly, rather than requiring a single bounded multiplication morphism, we work with compatible families of bounded left and right multiplication morphisms. Using Bin Gui's theory of categorical extensions, we associate to every discrete $C^*$-Frobenius algebra two (generally non-local) Möbius covariant extensions generated by left and right charged fields, respectively. If the discrete $C^*$-Frobenius algebra is commutative, the two extensions coincide and yield a local Möbius covariant extension. As applications, for every $C^*$-tensor category generated by an invertible object with trivial self-braiding such that its fusion product rule is given by $\\mathbb{Z}$, we construct two classes of examples: the simple current extension by $\\mathbb{Z}$ and the discrete Longo-Rehren construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14961",
  "author_total": 1,
  "authors": [
    {
      "name": "Ziyun Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpwsecpvxfwsq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14961",
  "fulltext_url": null,
  "id": "cpwsecpvxfwsq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14961",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213271831",
  "pdf_url": "https://arxiv.org/pdf/2609.14961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpwsecpvxfwsq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Discrete $C^*$-Frobenius Algebras and Infinite-Index Extensions in Algebraic Quantum Field Theories",
  "title_text": "Discrete C^*-Frobenius Algebras and Infinite-Index Extensions in Algebraic Quantum Field Theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/cpwsecpvxfwsq",
  "venue": "arXiv",
  "versions": []
}