Exploring de Sitter Space and Holography

摘要

We explore aspects of the physics of de Sitter (dS) space that are relevantto holography with a positive cosmological constant. First we display anonlocal map that commutes with the de Sitter isometries, transforms thebulk-boundary propagator and solutions of free wave equations in de Sitter ontothe same quantities in Euclidean anti-de Sitter (EAdS), and takes the twoboundaries 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 boundarydata. Third, we display a family of solutions to 3d gravity with a positivecosmological constant in which the equal time sections are arbitrary genusRiemann surfaces, and compute the action of these spaces as a functional ofboundary data from the Einstein gravity and Chern-Simons gravity points ofview. These studies suggest that if de Sitter space is dual to a Euclideanconformal field theory (CFT), this theory should involve two disjoint, butpossibly 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 topropose that a holographic dual description of de Sitter space would involve apure entangled state in a product of two of our unconventional CFTs associatedwith the de Sitter boundaries. This state can be constructed to preserve the deSitter symmetries and and its decomposition in a basis appropriate to antipodalinertial observers would lead to the thermal properties of static patch.