{
  "abstract": "It has been an open question whether there exist holomorphic VOAs with N=1 supersymmetry and Witten index 1 for any positive central charge c. The existence of such a theory with c=288 is closely related to the 576-periodicity of the TMF spectrum via the Segal-Stolz-Teichner conjecture. Here we report the construction of thousands of such theories by extending the approach initiated by Gaiotto and Johnson-Freyd via ternary codes. In addition, for every positive integer k, we also construct holomorphic N=1 VOAs of central charge c=12k with index 24/gcd(24,k) -- conjectured to be the minimum -- in a computer-aided search carried out by AI coding agents. We overcome the exponential-time barrier by using chains of smaller cells to build ternary codes, whose indices can then be evaluated via a transfer-matrix technique, and we use a symmetric orbifold construction to reduce the problem of k=12 and 24 to that of k=6. Along the way, we also establish several results on ternary codes and their indices. Using an observation relating codes and Landau-Ginzburg orbifold models, we argue that the non-chiral doubles of the ternary code VOAs can always be gapped supersymmetrically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33165",
  "author_total": 1,
  "authors": [
    {
      "name": "Du Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bk8gkjb63c3by.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33165",
  "fulltext_url": null,
  "id": "bk8gkjb63c3by",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33165",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223991590",
  "pdf_url": "https://arxiv.org/pdf/2610.33165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bk8gkjb63c3by.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Construction of holomorphic SCFTs with minimal index",
  "title_text": "Construction of holomorphic SCFTs with minimal index",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bk8gkjb63c3by",
  "venue": "arXiv",
  "versions": []
}