Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline

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.

1+26 pages, 1 figure. v2: citations added, minor clarifications and typos fixed

References in corpus (6)

• Micromanaging de Sitter holography
• A Holographic Framework for Eternal Inflation
• Quasinormal modes of D-dimensional de Sitter spacetime
• Hidden Conformal Symmetry and Quasi-normal Modes
• Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry
• A strong coupling expansion for N=4 SYM theory and other SCFT's

Cited by in corpus (74)

• Momentum dissipation and effective theories of coherent and incoherent transport
• Warped Conformal Field Theory
• Analyticity and Unitarity for Cosmological Correlators
• Late-time Structure of the Bunch-Davies De Sitter Wavefunction
• Holography for inflation using conformal perturbation theory
• Warped Conformal Field Theory as Lower Spin Gravity
• The Wave Function of Vasiliev's Universe - A Few Slices Thereof
• Infrared Realization of dS${}_2$ in AdS${}_2$
• Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems
• Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity
• State/Operator Correspondence in Higher-Spin dS/CFT
• de Sitter Microstates from $T\bar{T}+{\Lambda }_2$ and the Hawking-Page Transition
• De Sitter Horizons & Holographic Liquids
• The central dogma and cosmological horizons
• The Price of Curiosity: Information Recovery in de Sitter Space
• The Pauli exclusion principle at strong coupling: Holographic matter and momentum space
• Entanglement in De Sitter Space
• Black holes in dS${}_3$
• The minus sign in the first law of de Sitter horizons
• Holographic Complexity and de Sitter Space
• Chaos and complementarity in de Sitter space
• Higher Spin de Sitter Holography from Functional Determinants
• The Källén-Lehmann representation in de Sitter spacetime
• Liouville theory beyond the cosmological horizon
• Holographic Complexity in dS${}_{d+1}$
• Ladder Symmetries of Black Holes and de Sitter Space: Love Numbers and Quasinormal Modes
• Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics
• Incompressible Fluids of the de Sitter Horizon and Beyond
• Notes on Matrix Models
• Warped Entanglement Entropy
• On the quasinormal modes of the de Sitter spacetime
• The Cosmological Switchback Effect
• Tensors and Spinors in de Sitter Space
• Complex geodesics in de Sitter space
• Quasinormal Quantization in deSitter Spacetime
• Holographic Representation of Local Operators In De Sitter Space
• Charged Quantum Fields in AdS${}_2$
• Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging
• A microscopic realization of dS${}_3$
• Conformal quantum mechanics of causal diamonds
• Transient dynamics of quasinormal mode sums
• Bridging the static patches: de Sitter holography and entanglement
• Towards non-AdS Holography via the Long String Phenomenon
• Black Hole Scattering and Partition Functions
• Volume complexity of dS bubbles
• Gravitational Wilson Lines in 3D de Sitter
• (A)dS Holography with a Cut-off
• dS${}_2$ Supergravity
• Baby de Sitter Black Holes and dS${}_3$/CFT${}_2$
• Grassmann Matrix Quantum Mechanics
• Characters, quasinormal modes, and Schwinger pairs in $d{S}_2$ with flux
• One-dimensional Quantum Gravity and the Schwarzian theory
• Large N matrices from a nonlocal spin system
• MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch
• The Cosmological Switchback Effect II
• Vacuum thermal effects in flat space-time from conformal quantum mechanics
• Moduli Stabilization and the Holographic RG for AdS and dS
• Holographic quantization of linearized higher-spin gravity in the de Sitter causal patch
• A Modular Operator Approach to Entanglement of Causally Closed Regions
• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• Higher-spin realization of a dS static patch/cut-off CFT correspondence
• Shocks and Information Exchange in de Sitter Space
• Horizon causality from holographic scattering in asymptotically dS${}_3$
• Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+{\Lambda }_2$ Flow
• All the Stationary Vacuum States of De Sitter Space
• Conformal quantum mechanics and holographic quench
• De Sitter Horizon Edge Partition Functions
• The inverse spatial Laplacian of spherically symmetric spacetimes
• Real-time observables in de Sitter thermodynamics
• The Spectrum of Static Subtracted Geometries
• Enhanced symmetry and Entropy of Schwarzschild-deSitter spacetime
• Cosmology as a CFT${}_1$
• Gravitons on Nariai Edges
• Massive holographic QFTs in de Sitter