Holographic operator mapping in dS/CFT and cluster decomposition

Abstract

The bulk to boundary mapping for massive scalar fields is constructed, providing a de Sitter analog of the LSZ reduction formula. The set of boundary correlators thus obtained defines a potentially new class of conformal field theories based on principal series representations of the global conformal group. Conversely, we show bulk field operators in de Sitter may be reconstructed from boundary operators. While consistent at the level of the free field theory, the boundary CFT does not satisfy cluster decomposition. The resulting conformal field theory does not satisfy the basic axioms of Euclidean quantum field theory due to Osterwalder and Schrader, so is likely not well-defined once interactions are included.Comment: 16 pages, 1 figur