Quantum Liouville theory and BTZ black hole entropy

2003/10/25 by Yujun Chen
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #BTZ black hole #Black Holes and Theoretical Physics #Black hole thermodynamics #Conformal field theory #Conformal map #Decoupling (probability) #Entropy (arrow of time) #Lie algebra #Liouville field theory #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum field theory #Quantum gravity #Quantum mechanics #Relationship between string theory and quantum field theory #Root of unity #String theory #Verma module #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/21/4/028

published as Class.Quant.Grav. 21 (2004) 1153-1180 · LaTeX, 33 pages, 4 eps figures

arxiv created 2003/10/25 · openalex publication_date 2004/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 . 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 of the 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.

Citations

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