A Paradox and its Resolution Illustrate Principles of de Sitter Holography

TL;DR

The note analyzes a paradox in de Sitter holography where holographic real-valued correlators clash with semiclassical correlators that have real and imaginary components. It argues that time-reversal is a gauge symmetry in the bulk, requiring an observer with a clock to fix the gauge and recover semiclassical behavior. The resolution shows that gauge fixing—via forward or backward clock evolution—determines the presence of time-reversal-odd (imaginary) parts in correlators. This highlights the essential role of observers and quantum reference frames in a closed, gauge-theoretic cosmology and connects to holographic constructions like DSSYK∞ in de Sitter space.

Abstract

Semiclassical gravity and the holographic description of the static patch of de Sitter space appear to disagree about properties of correlation functions. Certain holographic correlation functions are necessarily real whereas their semiclassical counterparts have both real and imaginary parts. The resolution of this apparent contradiction involves the fact that time-reversal is a gauge symmetry in de Sitter space -- a point made by Harlow and Ooguri -- and the need for an observer (or quantum reference frame) as advocated by Chandrasekaran, Longo, Penington, and Witten.

Figures (1)

• Figure 1: Penrose diagram for de Sitter space. The dashed black curve is the stretched horizon of the right-side static patch. The dashed red curve shows a particle being emitted and absorbed by the stretched horizon.