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Cosmic ER=EPR in dS/CFT

Jordan Cotler, Andrew Strominger

TL;DR

This work extends the ER=EPR paradigm to global de Sitter space within dS/CFT by showing that the bulk exists as an entangled state of two boundary CFTs, with the Euclidean vacuum realized as a thermofield double at imaginary temperature. Using a quasinormal mode basis, the authors explicitly construct the bulk vacua, derive the northern density matrix as a thermal state of the static patch, and provide a precise boundary dual in terms of two coupled CFT$_3$s whose states form a thermofield double. The global dS$_4$ Hilbert space is shown to be isomorphic to the tensor product of two CFT$_3$ Hilbert spaces, with bulk operators and correlators expressible in terms of CFT$_3$ operators acting on both copies. The results illuminate how spacetime geometry and thermality emerge from quantum entanglement in holography and suggest connections to disorder-averaged CFT constructions and time's holographic emergence.

Abstract

In the dS/CFT correspondence, bulk states on global spacelike slices of de Sitter space are dual to (in general) entangled states in the tensor product of the dual CFT Hilbert space with itself. We show, using a quasinormal mode basis, that the Euclidean vacuum (for free scalars in a certain mass range) is a thermofield double state in the dual CFT description, and that the global de Sitter geometry emerges from quantum entanglement between two copies of the CFT. Tracing over one copy of the CFT produces a mixed thermal state describing a single static causal diamond.

Cosmic ER=EPR in dS/CFT

TL;DR

This work extends the ER=EPR paradigm to global de Sitter space within dS/CFT by showing that the bulk exists as an entangled state of two boundary CFTs, with the Euclidean vacuum realized as a thermofield double at imaginary temperature. Using a quasinormal mode basis, the authors explicitly construct the bulk vacua, derive the northern density matrix as a thermal state of the static patch, and provide a precise boundary dual in terms of two coupled CFTs whose states form a thermofield double. The global dS Hilbert space is shown to be isomorphic to the tensor product of two CFT Hilbert spaces, with bulk operators and correlators expressible in terms of CFT operators acting on both copies. The results illuminate how spacetime geometry and thermality emerge from quantum entanglement in holography and suggest connections to disorder-averaged CFT constructions and time's holographic emergence.

Abstract

In the dS/CFT correspondence, bulk states on global spacelike slices of de Sitter space are dual to (in general) entangled states in the tensor product of the dual CFT Hilbert space with itself. We show, using a quasinormal mode basis, that the Euclidean vacuum (for free scalars in a certain mass range) is a thermofield double state in the dual CFT description, and that the global de Sitter geometry emerges from quantum entanglement between two copies of the CFT. Tracing over one copy of the CFT produces a mixed thermal state describing a single static causal diamond.
Paper Structure (7 sections, 48 equations, 2 figures)

This paper contains 7 sections, 48 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quasinormal modes
  3. Vacua
  4. Northern density matrix
  5. Dual boundary description
  6. Discussion
  7. dS$_4$ Killing vectors

Figures (2)

  • Figure 1: A depiction of the regions of support of the real, complete set of modes $\Phi_{B}^{\text{FN}}$, $\Phi_{B}^{\text{PN}}$, $\Phi_{B}^{\text{FS}}$, $\Phi_{B}^{\text{PS}}$. Here $\text{N}$ and $\text{S}$ denote the northern and southern static patches of global dS$_4$, and $\text{F}$ and $\text{P}$ denote the future and past Milne regions.
  • Figure 2: The left-hand side depicts two $S^3$ partition functions (with operator insertions) of two CFTs, jointly disorder-averaged over some source to which they are coupled (dotted lines). The right-hand side depicts what happens when we break the spheres along an $S^2$ equator, arriving at two states which are each entangled between two CFTs. Here the dotted lines denote the entanglement between the CFTs.