Three-dimensional quantum geometry and black holes

Nov, 1998
39 pages
Published in:
  • AIP Conf.Proc. 484 (1999) 1, 147-169
  • Published: Jul 13, 1999
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Abstract:
We review some aspects of three-dimensional quantum gravity with emphasis in the `CFT -> Geometry' map that follows from the Brown-Henneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the Bekenstein-Hawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analysed in detail using a Hamiltonian Chern-Simons formalism.
Note:
  • 39 pages, Latex, no figures. Invited talk at the Second Meeting "Trends in Theoretical Physics", held in Buenos Aires, December, 1998. v2: References added and minor corrections. v3: An incorrect statement about the sign of the Chern-Simons level erased. Extended (and in some cases modified) discussions in most sections. References added
  • quantum gravity
  • space-time configurations
  • black holes
  • entropy
  • conformal symmetry
  • quantisation (quantum theory)
  • review: La Plata 1998/11/28
  • quantum gravity
  • dimension: 3
  • field theory: conformal