Spacetime from unentanglement

Yasunori Nomura (Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, California 94720, USA; Theoretical Physics Group, Lawrence Berkeley National Laboratory, California 94720, USA; Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan) ; Pratik Rath (Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, California 94720, USA; Theoretical Physics Group, Lawrence Berkeley National Laboratory, California 94720, USA) ; Nico Salzetta (Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, California 94720, USA; Theoretical Physics Group, Lawrence Berkeley National Laboratory, California 94720, USA)

The past decade has seen a tremendous effort toward unraveling the relationship between entanglement and emergent spacetime. These investigations have revealed that entanglement between holographic degrees of freedom is crucial for the existence of bulk spacetime. We examine this connection from the other end of the entanglement spectrum and clarify the assertion that maximally entangled states have no reconstructable spacetime. To do so, we first define the conditions for bulk reconstructability. Under these terms, we scrutinize two cases of maximally entangled holographic states. One is the familiar example of AdS black holes; these are dual to thermal states of the boundary conformal field theory. Sending the temperature to the cutoff scale makes the state maximally entangled and the respective black hole consumes the spacetime. We then examine the de Sitter limit of Friedmann-Robertson-Walker (FRW) spacetimes. This limit is maximally entangled if one formulates the boundary theory on the holographic screen. Paralleling the antiā€“de Sitter (AdS) black hole, we find the resulting reconstructable region of spacetime vanishes. Motivated by these results, we prove a theorem showing that maximally entangled states have no reconstructable spacetime. Evidently, the emergence of spacetime is endemic to intermediate entanglement. By studying the manner in which intermediate entanglement is achieved, we uncover important properties about the boundary theory of FRW spacetimes. With this clarified understanding, our final discussion elucidates the natural way in which holographic Hilbert spaces may house states dual to different geometries. This paper provides a coherent picture clarifying the link between spacetime and entanglement and develops many promising avenues of further work.

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      "source": "APS", 
      "value": "The past decade has seen a tremendous effort toward unraveling the relationship between entanglement and emergent spacetime. These investigations have revealed that entanglement between holographic degrees of freedom is crucial for the existence of bulk spacetime. We examine this connection from the other end of the entanglement spectrum and clarify the assertion that maximally entangled states have no reconstructable spacetime. To do so, we first define the conditions for bulk reconstructability. Under these terms, we scrutinize two cases of maximally entangled holographic states. One is the familiar example of AdS black holes; these are dual to thermal states of the boundary conformal field theory. Sending the temperature to the cutoff scale makes the state maximally entangled and the respective black hole consumes the spacetime. We then examine the de Sitter limit of Friedmann-Robertson-Walker (FRW) spacetimes. This limit is maximally entangled if one formulates the boundary theory on the holographic screen. Paralleling the anti\u2013de Sitter (AdS) black hole, we find the resulting reconstructable region of spacetime vanishes. Motivated by these results, we prove a theorem showing that maximally entangled states have no reconstructable spacetime. Evidently, the emergence of spacetime is endemic to intermediate entanglement. By studying the manner in which intermediate entanglement is achieved, we uncover important properties about the boundary theory of FRW spacetimes. With this clarified understanding, our final discussion elucidates the natural way in which holographic Hilbert spaces may house states dual to different geometries. This paper provides a coherent picture clarifying the link between spacetime and entanglement and develops many promising avenues of further work."
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Published on:
16 May 2018
Publisher:
APS
Published in:
Physical Review D , Volume 97 (2018)
Issue 10
DOI:
https://doi.org/10.1103/PhysRevD.97.106010
arXiv:
1711.05263
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: