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arXiv · 2610.31413

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 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.

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Eric Perlmutter. 2026-10-22. The Spectral Edge at Large Central Charge and Black Hole Statistics. https://arxiv.org/abs/2610.31413

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