{"title":"Algebraic ER=EPR and complexity transfer","authors":"Netta Engelhardt, Hong Liu","doi":"10.1007/jhep07(2024)013","DOIUrl":null,"url":null,"abstract":"<p>We propose an algebraic definition of ER=EPR in the <i>G</i><sub><i>N</i></sub> → 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 <i>the structure of entanglement</i>. 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 <span>\\( \\mathcal{O} \\)</span>(1<i>/G</i><sub><i>N</i></sub>) 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 III<sub>1</sub> 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.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of High Energy Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/jhep07(2024)013","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
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