Virasoro orbits, AdS3 quantum gravity and entropy

We analyse the canonical structure of AdS_3 gravity in terms of the coadjointorbits of the Virasoro group. There is one subset of orbits, associated to BTZblack hole solutions, that can be described by a pair of chiral free fieldswith a background charge. There is also a second subset of orbits, associatedto point-particle solutions, that are described by two pairs of chiral freefields obeying a constraint. All these orbits admit K\"ahler quantization andgenerate a Hilbert space which, despite of having $\Delta_0(\bar{\Delta}_0)=0$,does not provide the right degeneracy to account for the Bekenstein-Hawkingentropy due to the breakdown of modular invariance. Therefore, additionaldegrees of freedom, reestablishing modular invariance, are necessarily requiredto properly account for the black hole entropy.Comment: LaTex file, 12 pages. New references adde