CFT duals of three-dimensional de Sitter gravity

Abstract

We present a class of dS/CFT correspondence between two-dimensional CFTs and three-dimensional de Sitter spaces. We argue that such a CFT includes an SU(2) WZW model in the critical level limit k → −2, which corresponds to the classical gravity limit. We can generalize this dS/CFT by considering the SU(N) WZW model in the critical level limit k → −N, dual to the higher-spin gravity on a three-dimensional de Sitter space. We confirm that under this proposed duality the classical partition function in the gravity side can be reproduced from CFT calculations. We also point out a duality relation known in higher-spin holography provides further evidence. Moreover, we analyze two-point functions and entanglement entropy in our dS/CFT correspondence. Possible spectrum and quantum corrections in the gravity theory are discussed.