Mathematics – Quantum Algebra
Scientific paper
Feb 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cqgra..21.1153c&link_type=abstract
Classical and Quantum Gravity, Volume 21, Issue 4, pp. 1153-1180 (2004).
Mathematics
Quantum Algebra
10
Scientific paper
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_{\hq}(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 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.
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