{
  "abstract": "We identify a topological constraint on extremal $\\mathcal{N}=1$ AdS$_3$ spectra that is not implied by genus-one modular covariance of the three even spin structure partition functions. Assuming the expected topological modular forms divisibility of the Ramond Witten index, we show that for infinitely many odd $n$ at central charge $c=12n$, an extremal holomorphic $\\mathcal{N}=1$ superconformal field theory requires an odd number of Neveu--Schwarz primaries at the BTZ threshold. Thus the strict ansatz with no threshold primaries is excluded for this infinite family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17359",
  "author_total": 1,
  "authors": [
    {
      "name": "Yutaka Yoshida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1hbzkj6fctt2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17359",
  "fulltext_url": null,
  "id": "f1hbzkj6fctt2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17359",
  "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"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7213397967",
  "pdf_url": "https://arxiv.org/pdf/2609.17359",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1hbzkj6fctt2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.17359",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17359"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Topological Modular Forms Constrain Threshold States in Extremal $\\mathcal{N}=1$ AdS$_3$ Gravity",
  "title_text": "Topological Modular Forms Constrain Threshold States in Extremal 𝒩=1 AdS_3 Gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/f1hbzkj6fctt2",
  "venue": "arXiv",
  "versions": []
}