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 h ¯>h¯extr∼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 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 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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- December 2019
- DOI:
- 10.1007/JHEP12(2019)003
- arXiv:
- arXiv:1906.04416
- Bibcode:
- 2019JHEP...12..003M
- Keywords:
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- AdS-CFT Correspondence;
- Black Holes;
- Conformal and W Symmetry;
- Conformal Field Theory;
- High Energy Physics - Theory
- E-Print:
- doi:10.1007/JHEP12(2019)003