Timelike entanglement entropy
Abstract We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2023)052 |
| _version_ | 1827859799612588032 |
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| author | Kazuki Doi Jonathan Harper Ali Mollabashi Tadashi Takayanagi Yusuke Taki |
| author_facet | Kazuki Doi Jonathan Harper Ali Mollabashi Tadashi Takayanagi Yusuke Taki |
| author_sort | Kazuki Doi |
| collection | DOAJ |
| description | Abstract We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space. |
| first_indexed | 2024-03-12T13:14:51Z |
| format | Article |
| id | doaj.art-b7eed0e639c14c79930be68ccde474e3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:14:51Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b7eed0e639c14c79930be68ccde474e32023-08-27T11:05:24ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023516210.1007/JHEP05(2023)052Timelike entanglement entropyKazuki Doi0Jonathan Harper1Ali Mollabashi2Tadashi Takayanagi3Yusuke Taki4Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto UniversityCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto UniversityCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto UniversityCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto UniversityCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto UniversityAbstract We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space.https://doi.org/10.1007/JHEP05(2023)052AdS-CFT CorrespondenceModels of Quantum Gravity |
| spellingShingle | Kazuki Doi Jonathan Harper Ali Mollabashi Tadashi Takayanagi Yusuke Taki Timelike entanglement entropy Journal of High Energy Physics AdS-CFT Correspondence Models of Quantum Gravity |
| title | Timelike entanglement entropy |
| title_full | Timelike entanglement entropy |
| title_fullStr | Timelike entanglement entropy |
| title_full_unstemmed | Timelike entanglement entropy |
| title_short | Timelike entanglement entropy |
| title_sort | timelike entanglement entropy |
| topic | AdS-CFT Correspondence Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP05(2023)052 |
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