The ds/cft correspondence

Abstract

A holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I+ (the future boundary of dSD ) are mapped to the antipodal points on SD−1 relative to those on I− . For the case of dS3, which is analyzed in some detail, the central charge of the CFT2 is computed in an analysis of the asymptotic symmetry group at I± . This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be non-unitary and (if for example there are suf-ficently massive stable scalars) contain complex conformal weights. We also consider the physical region O− of dS3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. O− can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by L0 + ¯L0, and is dual to scale transformations in the boundary CFT2 .