Holographic operator mapping in dS/CFT and cluster decomposition

TL;DR

This paper develops a holographic mapping for de Sitter space, constructing boundary correlators from bulk fields, revealing a new class of conformal theories that lack cluster decomposition and may not be well-defined with interactions.

Contribution

It introduces a de Sitter holographic operator mapping analogous to LSZ, and explores the properties and limitations of the resulting boundary conformal field theories.

Findings

Boundary correlators form a new class of CFTs based on principal series representations.

Bulk operators can be reconstructed from boundary operators in de Sitter space.

The boundary CFT does not satisfy cluster decomposition or the axioms of Euclidean QFT.

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.