The Entropy of the BTZ Black Hole and AdS/CFT Correspondence

TL;DR

This paper develops a quantum description of the BTZ black hole using a boundary Wess-Zumino-Witten model, linking its entropy to the AdS/CFT correspondence and addressing the black hole entropy puzzle.

Contribution

It introduces a quantum action for the BTZ black hole via a boundary conformal field theory, providing new insights into its entropy and quantum nature.

Findings

Quantum action described by an SL(2,R) WZW model on the boundary.

Coupling affects the central charge of the Virasoro algebra.

Explanation of black hole entropy within the AdS/CFT framework.

Abstract

We construct an action, which governs the dynamics of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole and perform the canonical quantization. The quantum action is given by a $SL(2,R)$ Wess-Zumino-Witten model on the boundary coupled to the classical anti-de Sitter background, representing a massless BTZ black hole. The coupling, determined by a one-cocyle condition, is found to give dominant contribution to the central charge of Virasoro algebra. The entropy of the BTZ black hole is discussed from the point view of the AdS/CFT correspondence and an explanation is given to the puzzle of black hole entropy in the BTZ case. The BTZ black hole is a quantum object and the BTZ black hole with finite mass should be considered as a quantum excitation of the massless one.