Algebraic ER=EPR and complexity transfer
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13130_2024_Article_23850.pdf
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4.87 MB
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849b601cabc2fe124119f67eab86370c
Author(s)
Engelhardt, Netta
Liu, Hong
Date Issued
July 2, 2024
Journal
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Citation
Engelhardt, N., Liu, H. Algebraic ER=EPR and complexity transfer. J. High Energ. Phys. 2024, 13 (2024).
Version
Final published version
Abstract
We propose an algebraic definition of ER=EPR in the GN → 0 limit, which associates bulk spacetime connectivity/disconnectivity to the operator algebraic structure of a quantum gravity system. The new formulation not only includes information on the amount of entanglement, but also more importantly the structure of entanglement. We give an independent definition of a quantum wormhole as part of the proposal. This algebraic version of ER=EPR sheds light on a recent puzzle regarding spacetime disconnectivity in holographic systems with
O
$$ \mathcal{O} $$
(1/GN) entanglement. We discuss the emergence of quantum connectivity in the context of black hole evaporation and further argue that at the Page time, the black hole-radiation system undergoes a transition involving the transfer of an emergent type III1 subalgebra of high complexity operators from the black hole to radiation. We argue this is a general phenomenon that occurs whenever there is an exchange of dominance between two competing quantum extremal surfaces.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/jhep07(2024)013
