Some Aspects of the de Sitter/CFT Correspondence

TL;DR

This paper explores the de Sitter/CFT correspondence by deriving the central charge, calculating correlation functions, and analyzing the energy-momentum tensor and Casimir energy for dual conformal field theories, revealing bounds related to black hole mass.

Contribution

It provides new derivations of the central charge and correlation functions in the de Sitter/CFT framework, and analyzes bounds on black hole mass from the dual CFT perspective.

Findings

Derived the central charge from conformal anomaly and stress tensor transformations.

Computed two-point correlators for CFT operators in static coordinates.

Identified an upper bound on black hole mass for positive pressure, related to the Nariai solution.

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.