Algebraic ER=EPR and complexity transfer
Author(s)
Engelhardt, Netta; Liu, Hong
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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.
Date issued
2024-07-02Department
Massachusetts Institute of Technology. Center for Theoretical PhysicsJournal
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
ISSN
1029-8479