Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline

TL;DR

This paper reveals hidden SL(2,R) symmetries in de Sitter spacetime's static patch, linking propagators and quasinormal modes to conformal quantum mechanics, suggesting a duality with a worldline conformal theory.

Contribution

It uncovers the conformal symmetry structure of propagators in de Sitter space and proposes a dual description via conformal quantum mechanics.

Findings

Propagators are governed by SL(2,R) symmetries at all frequencies.

Quasinormal modes are generated by SL(2,R) actions.

Enhanced supersymmetry appears for specific fields in 4D.

Abstract

We show that the propagators of gravitons and scalar fields seen by a static patch observer in de Sitter spacetime are controlled by hidden SL(2,R) symmetries, at all frequencies. The retarded Green's function is determined by an SL(2,R) x SL(2,R) action generated by conformal Killing vectors of de Sitter spacetime times a line. This observation uses the fact that the static patch of dS_{d+1} x R is conformal to the hyperbolic patch of AdS_3 x S^{d-1}. The poles of the propagators, the quasinormal frequencies, are generated by associated SL(2,R) actions. The quasinormal mode generating algebras capture the conformal weights more usually read off from the fields at future and past infinity. For conformally coupled scalar fields, and for gravitons in four dimensions, this SL(2,R) algebra has an enhanced supersymmetric structure and is generated by particular conformal Killing vectors of de Sitter spacetime. We show how the worldline de Sitter propagators can be reproduced from a `level matched' left and right moving conformal quantum mechanics with an appropriate spectrum of primary operators. Our observations are consistent with the notion that the static patch of de Sitter spacetime is dually described by a (level matched) large N worldline conformal quantum mechanics.