Virasoro Orbits, AdS_3 Quantum Gravity and Entropy

Details Virasoro Orbits, AdS_3 Quantum Gravity and Entropy Virasoro Orbits, AdS_3 Quantum Gravity and Entropy

1999-03-29

arxiv.org/abs/hep-th/9903248v2

JHEP 9905 (1999) 009

Physics

High Energy Physics

High Energy Physics - Theory

LaTex file, 12 pages. New references added

Scientific paper

10.1088/1126-6708/1999/05/009

We analyse the canonical structure of AdS_3 gravity in terms of the coadjoint orbits of the Virasoro group. There is one subset of orbits, associated to BTZ black hole solutions, that can be described by a pair of chiral free fields with a background charge. There is also a second subset of orbits, associated to point-particle solutions, that are described by two pairs of chiral free fields obeying a constraint. All these orbits admit K\"ahler quantization and generate a Hilbert space which, despite of having $\Delta_0(\bar{\Delta}_0)=0$, does not provide the right degeneracy to account for the Bekenstein-Hawking entropy due to the breakdown of modular invariance. Therefore, additional degrees of freedom, reestablishing modular invariance, are necessarily required to properly account for the black hole entropy.

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