Quantum Liouville theory and BTZ black hole entropy

Abstract

In this paper I give an explicit conformal field theory description of (2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field theory I investigate the reducible Verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra U_q(sl_2) \odot U_{\hat{q}}(sl_2). I show that there are states that decouple from these reducible Verma modules in a similar fashion to the decoupling of null states in minimal models. Because ofthe nonstandard form of the Ward identity for the two-point correlation functions in quantum Liouville field theory, these decoupling states have positive-definite norms. The explicit counting from these states gives the desired Bekenstein-Hawking entropy in the semi-classical limit when q is a root of unity of odd order.

arXiv commentLaTeX, 33 pages, 4 eps figures

References in corpus (23)

• The Black Hole in Three Dimensional Space Time
• Black Hole Entropy from Near-Horizon Microstates
• Two and three-point functions in Liouville theory
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Quantum effective action from the AdS/CFT correspondence
• Conformal description of horizon's states
• Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes
• What We Don't Know about BTZ Black Hole Entropy
• Global Charges in Chern-Simons theory and the 2+1 black hole
• On Correlation Functions for Non-critical Strings with c<1 but d>1
• Entropy of Three-Dimensional Black Holes in String Theory
• 3D Gravity, Point Particles and Liouville Theory
• Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity
• Near Horizon Geometry and Black Holes in Four Dimensions
• Gravity-Matter Couplings from Liouville Theory
• Liouville Theory: Quantum Geometry of Riemann Surfaces
• Quasitriangularity of quantum groups at roots of 1
• Uniqueness of the asymptotic AdS3 geometry
• The Braiding of Chiral Vertex Operators with Continuous Spins in 2D Gravity
• Black hole entropy from classical Liouville theory
• Equivalence of Geometric h<1/2 and Standard c>25 Approaches to Two-Dimensional Quantum Gravity
• Liouville Theory: Ward Identities for Generating Functional and Modular Geometry
• Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

Cited by in corpus (25)

• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Conformal Bootstrap, Universality and Gravitational Scattering
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity
• Horizon Constraints and Black Hole Entropy
• Horizon constraints and black hole entropy
• Effective Conformal Descriptions of Black Hole Entropy
• Rotating Boson Stars in 2+1 Dimensions
• Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity
• Black Hole Thermodynamics and Statistical Mechanics
• The Holographic Ward identity: Examples from 2+1 gravity
• Non-Quasinormal Modes and Black Hole Physics
• Fate of Three-Dimensional Black Holes Coupled to a Scalar Field and the Bekenstein-Hawking Entropy
• Entanglement entropy in Jackiw-Teitelboim Gravity
• Indication for unsmooth horizon induced by quantum gravity interaction
• Horizons, Constraints, and Black Hole Entropy
• CFT description of three-dimensional Hawking-Page transition
• A Note on Black Hole Entropy in Loop Quantum Gravity
• Poisson Algebra of Diffeomorphism Generators in a Spacetime Containing a Bifurcation
• Reduction of BTZ spacetime to hypersurfaces of foliation
• Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity
• Thermodynamics of nonspherical black holes from Liouville theory
• Two Dimensional Conformal Symmetry and the Microscopic Interpretation of Black Hole Entropy
• Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory