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

Abstract

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 h ¯ $$ \overline{h} $$ > h ¯ extr $$ {\overline{h}}_{\mathrm{extr}} $$ ∼ c − 1 24 $$ \frac{c-1}{24} $$ , 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 h ¯ extr $$ {\overline{h}}_{\mathrm{extr}} $$ 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, h ¯ extr $$ {\overline{h}}_{\mathrm{extr}} $$ 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 → ∞ limit.

Keywords

• AdS-CFT Correspondence
• Black Holes
• Conformal and W Symmetry
• Conformal Field Theory