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PreprintCC BY 4.0arXiv

The Spectral Edge at Large Central Charge and Black Hole Statistics

  • Eric Perlmutter
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Abstract

We introduce a new approach to high-energy spectra in AdS3/CFT2, 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 Δ1 be the conformal dimension of the lightest excited Virasoro primary of a unitary CFT of central charge c, we show that Δ1 − c−1over 12 ≤ 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 Δ1 − c−1over 12 ≤ O(1). The result applies to theories with logarithmic rigidity of spectral counting fluctuations, as in random matrix theory.

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Cite

BibTeXRIS
BibTeX
@misc{perlmutter2026spectral,
  title = {{The Spectral Edge at Large Central Charge and Black Hole Statistics}},
  author = {Eric Perlmutter},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31413},
  eprint = {2610.31413},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31413},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Spectral Edge at Large Central Charge and Black Hole Statistics
AU  - Eric Perlmutter
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31413
UR  - https://arxiv.org/abs/2610.31413
AB  - 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−1over 12 ≤ 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−1over 12 ≤ O(1). The result applies to theories with logarithmic rigidity of spectral counting fluctuations, as in random matrix theory.
ER  -