Holography and quantum states in elliptic de Sitter space

TL;DR

This paper explores the holographic interpretation of higher-spin theories in elliptic de Sitter space, analyzing observer-dependent quantum states and deriving operator algebras from boundary conformal field theories.

Contribution

It proposes a framework for understanding higher-spin dS/CFT in elliptic de Sitter space, linking antipodal symmetry to boundary encodings and observer-dependent quantum physics.

Findings

Derived observer's operator algebra and Hamiltonian from boundary CFT.

Analyzed quantum states in non-time-orientable elliptic de Sitter space.

Identified limitations in deriving the S-matrix for observers.

Abstract

We outline a program for interpreting the higher-spin dS/CFT model in terms of physics in the causal patch of a dS observer. The proposal is formulated in "elliptic" de Sitter space dS_4/Z_2, obtained by identifying antipodal points in dS_4. We discuss recent evidence that the higher-spin model is especially well-suited for this, since the antipodal symmetry of bulk solutions has a simple encoding on the boundary. For context, we test some other (free and interacting) theories for the same property. Next, we analyze the notion of quantum field states in the non-time-orientable dS_4/Z_2. We compare the physics seen by different observers, with the outcome depending on whether they share an arrow of time. Finally, we implement the marriage between higher-spin holography and observers in dS_4/Z_2, in the limit of free bulk fields. We succeed in deriving an observer's operator algebra and Hamiltonian from the CFT, but not her S-matrix. We speculate on the extension of this to interacting higher-spin theory.