Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline

TL;DR

The work reveals a hidden conformal structure in the de Sitter static patch, showing that retarded propagators for gravitons and scalars are governed by $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ actions arising from a conformal relation to AdS$_3$. Quasinormal modes organize into $SL(2,\mathbb{R})$-generated ladders, with masses determining conformal weights that match expectations from infinity; for conformally coupled scalars and four-dimensional gravitons the structure enhances to a supersymmetric-like algebra. The authors embed the problem in an auxiliary AdS$_3$ setup and connect the Green's function to a level-matched left-right moving conformal quantum mechanics, suggesting a 0+1D holographic dual for the static patch. A concrete free-eigenvalue toy model illustrates how the $SL(2,\mathbb{R})$ symmetry controls correlators, and the framework invites a deeper exploration of a finite-temperature, large-N worldline dual for de Sitter holography.

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.

Figures (1)

• Figure 1: Quasinormal mode lowering operators when $x = {{1\over2}}$. In addition to the $J_-$ operators, the lowering operator $Q_-$ maps the two families of quasinormal modes into each other.