Quantum Liouville theory and BTZ black hole entropy

Details Quantum Liouville theory and BTZ black hole entropy Quantum Liouville theory and BTZ black hole entropy

2003-10-25

arxiv.org/abs/hep-th/0310234v1

Class.Quant.Grav. 21 (2004) 1153-1180

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 33 pages, 4 eps figures

Scientific paper

10.1088/0264-9381/21/4/028

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.

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