{
  "abstract": "We observe an apparently universal behavior in large $N$ conformal field theory (CFT) in $d\\geq 2$ dimensions: the single-trace, higher-spin gap obeys the parametric bound $Δ_{\\rm gap} \\lesssim (δc)^{1/d}$, where $δc$ is the central charge increment between successive theories. The origin of this bound is explained heuristically, using a generalized notion of branes that interpolate between conformal points in theory space. Seeking a more precise framework for this picture leads to the central concept of families of CFTs, which tacitly underlies various features and puzzles of AdS/CFT. We develop a working definition of families, with inspiration from families of $L$-functions in number theory, and formulate a family-level version of the gap bound. Interpreted holographically for families of AdS$_{d+1}$ vacua, this bound, when applicable, rules out Planckian scale separation, constrains the size and number of extra dimensions, and explains simple scaling patterns in string/M-theory. It also accounts for why all known large $N$ vector models have a bounded gap.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24496",
  "author_total": 1,
  "authors": [
    {
      "name": "Eric Perlmutter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fk287x0xjk0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24496",
  "fulltext_url": null,
  "id": "8fk287x0xjk0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24496",
  "language": "en",
  "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"
    ],
    [
      "hal",
      "0.phys"
    ],
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      "hal",
      "1.phys.hthe"
    ],
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      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223064795",
  "pdf_url": "https://arxiv.org/pdf/2610.24496",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fk287x0xjk0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24496",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24496"
    },
    {
      "first_seen": "2026-11-04T12:20:52Z",
      "native_id": "hal-05850392",
      "source": "hal",
      "url": "https://hal.science/hal-05850392v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Gravity as Large Scale Structure: Families of CFTs and the Higher-Spin Gap",
  "title_text": "Gravity as Large Scale Structure: Families of CFTs and the Higher-Spin Gap",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:12Z",
  "url": "https://research.draconitic.com/paper/8fk287x0xjk0g",
  "venue": "arXiv",
  "versions": []
}