Some Aspects of the de Sitter/CFT Correspondence

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 dS3 in planar coordinates to dS3 with cosmological horizon. The two-point correlator for CFT operators coupling to bulk scalars is obtained in cosmological coordinates, corresponding to a CFT on a cylinder. We furthermore compute the energy momentum tensor of the CFT 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. ∗[email protected]