Some Aspects of the de Sitter/CFT Correspondence
Dietmar Klemm
TL;DR
Addresses how quantum gravity on de Sitter space can be encoded in a Euclidean CFT living on the boundary. The paper derives the dS$_3$ central charge $c=\frac{3l}{2G}$ by both the conformal anomaly and the stress-tensor transformation from planar to cylindrical coordinates, and computes two-point correlators for bulk-scalar coupled operators in static and hyperbolic slicings. It further analyzes the five-dimensional Schwarzschild–de Sitter solution, deriving the CFT stress tensor and Casimir energy, and shows a positive-pressure bound on the black hole mass coinciding with the Nariai limit, echoing a reality bound on conformal weights. Together, these results bolster a concrete, calculable version of the dS/CFT correspondence and illuminate how holography handles horizons and cosmological constants.
Abstract
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.