Small Black Holes and Near-Extremal CFTs

Understand

Pure theories of AdS$_3$ quantum gravity are conjectured to be dual to CFTs with sparse spectra of light primary operators.

• The sparsest possible spectrum consistent with modular invariance includes only black hole states above the vacuum.
• Witten conjectured the existence of a family of extremal CFTs, which realize this spectrum for all admissible values of the central charge.
• We consider the quantum corrections to the classical spectrum, and propose a specific modification of Witten's conjecture which takes into account the existence of "small" black hole states.