Exploring de Sitter Space and Holography

TL;DR

This paper investigates the holographic duality of de Sitter space, proposing a novel dual CFT structure involving entangled states with unusual hermiticity, and explores the mathematical mappings between de Sitter and Euclidean AdS spaces.

Contribution

It introduces a nonlocal map linking de Sitter and Euclidean AdS physics, and proposes a new holographic dual involving entangled, unconventional CFTs with unique hermiticity conditions.

Findings

A nonlocal map relates dS and EAdS bulk-boundary propagators.

Scalar field actions in dS are expressed as boundary functionals.

A family of 3D gravity solutions with arbitrary genus boundaries is analyzed.

Abstract

We explore aspects of the physics of de Sitter (dS) space that are relevant to holography with a positive cosmological constant. First we display a nonlocal map that commutes with the de Sitter isometries, transforms the bulk-boundary propagator and solutions of free wave equations in de Sitter onto the same quantities in Euclidean anti-de Sitter (EAdS), and takes the two boundaries of dS to the single EAdS boundary via an antipodal identification. Second we compute the action of scalar fields on dS as a functional of boundary data. Third, we display a family of solutions to 3d gravity with a positive cosmological constant in which the equal time sections are arbitrary genus Riemann surfaces, and compute the action of these spaces as a functional of boundary data from the Einstein gravity and Chern-Simons gravity points of view. These studies suggest that if de Sitter space is dual to a Euclidean conformal field theory (CFT), this theory should involve two disjoint, but possibly entangled factors. We argue that these CFTs would be of a novel form, with unusual hermiticity conditions relating left movers and right movers. After exploring these conditions in a toy model, we combine our observations to propose that a holographic dual description of de Sitter space would involve a pure entangled state in a product of two of our unconventional CFTs associated with the de Sitter boundaries. This state can be constructed to preserve the de Sitter symmetries and and its decomposition in a basis appropriate to antipodal inertial observers would lead to the thermal properties of static patch.