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 \( \mathcal{O} \)(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.
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Acknowledgments
It is a pleasure to thank C. Gomez, D. Harlow, A. Karch, J. Kudler-Flam, S. Leutheusser, J. Maldacena, D. Marolf, N. Paquette, J. Sorce, A. Speranza, and E. Witten for helpful discussions. The work of NE is in part by the U.S. Department of Energy under Early Career Award DE-SC0021886, by the John Templeton Foundation via the Black Hole Initiative, by the Sloan Foundation, by the Heising-Simons Foundation, and by funds from the MIT physics department. The work of HL is supported by the Office of High Energy Physics of U.S. Department of Energy under grant Contract Number DE-SC0012567 and DE-SC0020360 (MIT contract # 578218).
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Engelhardt, N., Liu, H. Algebraic ER=EPR and complexity transfer. J. High Energ. Phys. 2024, 13 (2024). https://doi.org/10.1007/JHEP07(2024)013
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DOI: https://doi.org/10.1007/JHEP07(2024)013