Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-06-26
Nucl.Phys. B625 (2002) 295-311
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX, 1 figure. v4: Note added, final version to appear in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(02)00007-X
We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories. The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter space is derived both from the conformal anomaly and the transformation law of the CFT stress tensor when going from dS_3 in planar coordinates to dS_3 with cosmological horizon. The two-point correlator for CFT operators coupling to bulk scalars is obtained in static coordinates, corresponding to a CFT on a cylinder. Correlation functions are also computed for CFTs on two-dimensional hyperbolic space. We furthermore determine the energy momentum tensor and the Casimir energy of the conformal field theory dual to the Schwarzschild-de Sitter solution in five dimensions. Requiring the pressure to be positive yields an upper bound for the black hole mass, given by the mass of the Nariai solution. Beyond that bound, which is similar to the one found by Strominger requiring the conformal weights of CFT operators to be real, one encounters naked singularities.
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