A canonical purification for the entanglement wedge cross-section
Abstract In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2021)178 |
| _version_ | 1818677725180723200 |
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| author | Souvik Dutta Thomas Faulkner |
| author_facet | Souvik Dutta Thomas Faulkner |
| author_sort | Souvik Dutta |
| collection | DOAJ |
| description | Abstract In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo. |
| first_indexed | 2024-12-17T09:03:56Z |
| format | Article |
| id | doaj.art-f5908a7bd1b24f9b9097829c8915f968 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T09:03:56Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f5908a7bd1b24f9b9097829c8915f9682022-12-21T21:55:37ZengSpringerOpenJournal of High Energy Physics1029-84792021-03-012021314910.1007/JHEP03(2021)178A canonical purification for the entanglement wedge cross-sectionSouvik Dutta0Thomas Faulkner1Department of Physics, University of IllinoisDepartment of Physics, University of IllinoisAbstract In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.https://doi.org/10.1007/JHEP03(2021)178AdS-CFT CorrespondenceConformal Field TheoryRenormalization Group |
| spellingShingle | Souvik Dutta Thomas Faulkner A canonical purification for the entanglement wedge cross-section Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory Renormalization Group |
| title | A canonical purification for the entanglement wedge cross-section |
| title_full | A canonical purification for the entanglement wedge cross-section |
| title_fullStr | A canonical purification for the entanglement wedge cross-section |
| title_full_unstemmed | A canonical purification for the entanglement wedge cross-section |
| title_short | A canonical purification for the entanglement wedge cross-section |
| title_sort | canonical purification for the entanglement wedge cross section |
| topic | AdS-CFT Correspondence Conformal Field Theory Renormalization Group |
| url | https://doi.org/10.1007/JHEP03(2021)178 |
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