Small Black Holes and Near-Extremal CFTs

TL;DR

This paper explores quantum corrections to the spectrum of pure AdS$_3$ gravity duals, proposing a modified extremal CFT model that includes small black hole states with entropy from loop effects, consistent with supersymmetry.

Contribution

It introduces a new conjecture for near-extremal CFTs that accounts for quantum effects and small black hole states, extending Witten's extremal CFT framework.

Findings

Quantum corrections modify the classical spectrum.

Small black hole states have zero classical horizon area.

The conjecture aligns with supersymmetric theories and evades previous no-go results.

Abstract

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. These have zero classical horizon area, with a calculable entropy attributed solely to loop effects. Our conjecture passes various consistency checks, especially when generalized to include theories with supersymmetry. In theories with $\mathcal{N}=2$ supersymmetry, this "near-extremal CFT" proposal precisely evades the no-go results of Gaberdiel et al.