{
  "abstract": "We numerically study the space of compact unitary two-dimensional conformal field theories (2d CFTs) with central charge $c>1$ using the modular bootstrap. We focus on bounding the spectral gap $Δ_{\\rm gap}$ of such theories, namely the smallest scaling dimension among the non-vacuum primary operators. We use both a primal method that directly searches for consistent spectra and a dual method that yields rigorous exclusions. A key feature of our analysis is requiring the degeneracies of primary operators to be positive integers. At $c$ very near $1$, the integrality constraint greatly reduces the allowed spectral gap in both methods. For example, at $c-1 = 3\\times 10^{-3}$ integrality strengthens the rigorous bound from $Δ_{\\rm gap} \\lesssim 0.5$ to $Δ_{\\rm gap} < 0.041$. Our results suggest that the spectral gap might vanish as $c$ approaches $1$ from above.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07011",
  "author_total": 4,
  "authors": [
    {
      "name": "Nathan Benjamin"
    },
    {
      "name": "Kevin Langhoff"
    },
    {
      "name": "Wei Li"
    },
    {
      "name": "Jesse Thaler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vmh3gd0a5bsf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07011",
  "fulltext_url": null,
  "id": "6vmh3gd0a5bsf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07011",
  "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-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07011",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vmh3gd0a5bsf.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07011",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07011"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Constraining the spectral gap of 2d CFTs just above c=1",
  "title_text": "Constraining the spectral gap of 2d CFTs just above c=1",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:39Z",
  "url": "https://research.draconitic.com/paper/6vmh3gd0a5bsf",
  "venue": "arXiv",
  "versions": []
}