Virasoro Orbits, AdS_3 Quantum Gravity and Entropy

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.Comment: LaTex file, 12 pages. New references adde

Reflexive functors of modules in Commutative Algebra

Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors

A Note on Einstein Gravity on AdS3_3 and Boundary Conformal Field Theory

We find a simple relation between the first subleading terms in the asymptotic expansion of the metric field in AdS$_3$, obeying the Brown-Henneaux boundary conditions, and the stress tensor of the underlying Liouville theory on the boundary. We can also provide an more explicit relation between the bulk metric and the boundary conformal field theory when it is described in terms of a free field with a background charge.Comment: LateX file, 10 page

Majorana vs Pseudo-Dirac Neutrinos at the ILC

Neutrino masses could originate in seesaw models testable at colliders, with light mediators and an approximate lepton number symmetry. The minimal model of this type contains two quasi-degenerate Majorana fermions forming a pseudo-Dirac pair. An important question is to what extent future colliders will have sensitivity to the splitting between the Majorana components, since this quantity signals the breaking of lepton number and is connected to the light neutrino masses. We consider the production of these neutral heavy leptons at the ILC, where their displaced decays provide a golden signal: a forward-backward charge asymmetry, which depends crucially on the mass splitting between the two Majorana components. We show that this observable can constrain the mass splitting to values much lower than current bounds from neutrinoless double beta decay and natural loop corrections.Comment: 16 pages, 5 figures; v2: Minor changes, version accepted for publication in EPJ

Symmetries in two-dimensional dilaton gravity with matter

The symmetries of generic 2D dilaton models of gravity with (and without) matter are studied in some detail. It is shown that $\delta_2$, one of the symmetries of the matterless models, can be generalized to the case where matter fields of any kind are present. The general (classical) solution for some of these models, in particular those coupled to chiral matter, which generalizes the Vaidya solution of Einstein Gravity, is also given.Comment: Minor changes have been made; the references have been updated and some added; 11 pages. To appear in Phys. Rev.

Supermassive Black Holes and Galaxy Formation

The formation of supermassive black holes (SMBH) is intimately related to galaxy formation, although precisely how remains a mystery. I speculate that formation of, and feedback from, SMBH may alleviate problems that have arisen in our understanding of the cores of dark halos of galaxies.Comment: Talk at conference on Matter in the Universe, March 2001, ISSI Ber

Integrable models, degenerate horizons and AdS_2 black holes

The near extremal Reissner-Nordstrom black holes in arbitrary dimensions ca be modeled by the Jackiw-Teitelboim (JT) theory. The asymptotic Virasoro symmetry of the corresponding JT model exactly reproduces, via Cardy's formula, the deviation of the Bekenstein-Hawking entropy of the Reissner-Nordstrom black holes from extremality. We also comment how can we extend this approach to investigate the evaporation process.Comment: 4 pages, LaTeX file, uses espcrc2.sty. Talk given at the Third Conference on Constrained Dynamics and Quantum Gravit