Covariant bit threads
Abstract We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2023)180 |
| _version_ | 1797647492553113600 |
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| author | Matthew Headrick Veronika E. Hubeny |
| author_facet | Matthew Headrick Veronika E. Hubeny |
| author_sort | Matthew Headrick |
| collection | DOAJ |
| description | Abstract We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form U subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of A and its complement. The V-flow formula is the covariant version of the Freedman-Headrick bit thread reformulation of the Ryu-Takayanagi formula. We also introduce a measure-theoretic concept of a “thread distribution”, and explain how Riemannian flows, V-flows, and U-flows can be expressed in terms of thread distributions. |
| first_indexed | 2024-03-11T15:18:21Z |
| format | Article |
| id | doaj.art-9a2cc4415f324d2f92e7598c4a4287f1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T15:18:21Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9a2cc4415f324d2f92e7598c4a4287f12023-10-29T12:06:38ZengSpringerOpenJournal of High Energy Physics1029-84792023-07-012023719010.1007/JHEP07(2023)180Covariant bit threadsMatthew Headrick0Veronika E. Hubeny1Martin Fisher School of Physics, Brandeis UniversityCenter for Quantum Mathematics and Physics (QMAP), Department of Physics & Astronomy, University of CaliforniaAbstract We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form U subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of A and its complement. The V-flow formula is the covariant version of the Freedman-Headrick bit thread reformulation of the Ryu-Takayanagi formula. We also introduce a measure-theoretic concept of a “thread distribution”, and explain how Riemannian flows, V-flows, and U-flows can be expressed in terms of thread distributions.https://doi.org/10.1007/JHEP07(2023)180AdS-CFT CorrespondenceBlack HolesDifferential and Algebraic Geometry |
| spellingShingle | Matthew Headrick Veronika E. Hubeny Covariant bit threads Journal of High Energy Physics AdS-CFT Correspondence Black Holes Differential and Algebraic Geometry |
| title | Covariant bit threads |
| title_full | Covariant bit threads |
| title_fullStr | Covariant bit threads |
| title_full_unstemmed | Covariant bit threads |
| title_short | Covariant bit threads |
| title_sort | covariant bit threads |
| topic | AdS-CFT Correspondence Black Holes Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP07(2023)180 |
| work_keys_str_mv | AT matthewheadrick covariantbitthreads AT veronikaehubeny covariantbitthreads |