Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap

Abstract

Any unitary compact two-dimensional CFT with $c>1$ and no symmetries beyond Virasoro has a parametrically large density of primary states at large spin for $\bar{h}>{\bar{h}}_{\text{extr}}\sim \frac{c-1}{24}$, of a universal form determined by modular invariance. By including the contribution of light primary operators and multi-twist composites constructed from them in the modular bootstrap, we find that ${\bar{h}}_{\text{extr}}$ receives corrections in a large spin expansion, which we compute at finite $c$. The analysis uses a formulation of the modular S-transform as a Fourier transform acting on the density of primary states. For theories with gravitational duals, ${\bar{h}}_{\text{extr}}$ is interpreted as the extremality bound of rotating BTZ black holes, receiving quantum corrections which we compute at one loop by prohibiting naked singularities in the quantum-corrected geometry. This gravity result is reproduced by modular bootstrap in a semiclassical $c\to \infty$ limit.

References in corpus (4)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Entanglement entropy in three dimensional gravity

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