{
  "abstract": "We introduce a new approach to high-energy spectra in AdS$_3$/CFT$_2$, addressing the open challenge of incorporating spectral statistics into the modular bootstrap. Using the analytic theory of $L$-functions attached to two-dimensional CFTs, we leverage modular constraints among high-energy states to derive a sum rule relating the spectral edge to bulk spectral fluctuations. As an application, we establish a refined modular bootstrap bound: letting $Δ_1$ be the conformal dimension of the lightest excited Virasoro primary of a unitary CFT of central charge $c$, we show that $Δ_1 - {c-1\\over 12} \\leq o(c)$, with at most one exceptional value of the scalar gap at each sufficiently large $c$; moreover, along any sequence in $c$ for which such exceptional gaps are realized, the remaining gaps obey the stronger bound $Δ_1 - {c-1\\over 12} \\leq O(1)$. The result applies to theories with logarithmic rigidity of spectral counting fluctuations, as in random matrix theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31413",
  "author_total": 1,
  "authors": [
    {
      "name": "Eric Perlmutter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2h272k0ac72np.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31413",
  "fulltext_url": null,
  "id": "2h272k0ac72np",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31413",
  "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"
    ],
    [
      "hal",
      "1.phys.hthe"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223416412",
  "pdf_url": "https://arxiv.org/pdf/2610.31413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2h272k0ac72np.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31413"
    },
    {
      "first_seen": "2026-11-04T12:20:53Z",
      "native_id": "hal-05851342",
      "source": "hal",
      "url": "https://hal.science/hal-05851342v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Spectral Edge at Large Central Charge and Black Hole Statistics",
  "title_text": "The Spectral Edge at Large Central Charge and Black Hole Statistics",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:12Z",
  "url": "https://research.draconitic.com/paper/2h272k0ac72np",
  "venue": "arXiv",
  "versions": []
}