Replica wormholes and entanglement islands in the Karch-Randall braneworld
Abstract The Karch-Randall braneworld provides a natural set-up to study the Hawking radiation from a black hole using holographic tools. Such a black hole lives on a brane and is highly quantum yet has a holographic dual as a higher dimensional classical theory that lives in the ambient space. More...
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2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)063 |
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| author | Hao Geng |
| author_facet | Hao Geng |
| author_sort | Hao Geng |
| collection | DOAJ |
| description | Abstract The Karch-Randall braneworld provides a natural set-up to study the Hawking radiation from a black hole using holographic tools. Such a black hole lives on a brane and is highly quantum yet has a holographic dual as a higher dimensional classical theory that lives in the ambient space. Moreover, such a black hole is coupled to a nongravitational bath which is absorbing its Hawking radiation. This allows us to compute the entropy of the Hawking radiation by studying the bath using the quantum extremal surface prescription. The quantum extremal surface geometrizes into a Ryu-Takayanagi surface in the ambient space. The topological phase transition of the Ryu-Takayanagi surface in time from connecting different portions of the bath to the one connecting the bath and the brane gives the Page curve of the Hawking radiation that is consistent with unitarity. Nevertheless, there doesn’t exit a derivation of the quantum extremal surface prescription and its geometrization in the Karch-Randall braneworld. In this paper, we fill this gap. We mainly focus on the case that the ambient space is (2+1)-dimensional for which explicit computations can be done in each description of the set-up. We show that the topological phase transition of the Ryu-Takayanagi surface corresponds to the formation of the replica wormhole on the Karch-Randall brane as the dominant contribution to the replica path integral. For higher dimensional situations, we show that the geometry of the brane satisfies Einstein’s equation coupled with conformal matter. We comment on possible implications to the general rule of gravitational path integral from this equation. |
| format | Article |
| id | doaj-art-00370fa96bbe43a18f92adc8cf3aef98 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-00370fa96bbe43a18f92adc8cf3aef982025-01-19T12:07:16ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025113310.1007/JHEP01(2025)063Replica wormholes and entanglement islands in the Karch-Randall braneworldHao Geng0Center for the Fundamental Laws of Nature, Harvard UniversityAbstract The Karch-Randall braneworld provides a natural set-up to study the Hawking radiation from a black hole using holographic tools. Such a black hole lives on a brane and is highly quantum yet has a holographic dual as a higher dimensional classical theory that lives in the ambient space. Moreover, such a black hole is coupled to a nongravitational bath which is absorbing its Hawking radiation. This allows us to compute the entropy of the Hawking radiation by studying the bath using the quantum extremal surface prescription. The quantum extremal surface geometrizes into a Ryu-Takayanagi surface in the ambient space. The topological phase transition of the Ryu-Takayanagi surface in time from connecting different portions of the bath to the one connecting the bath and the brane gives the Page curve of the Hawking radiation that is consistent with unitarity. Nevertheless, there doesn’t exit a derivation of the quantum extremal surface prescription and its geometrization in the Karch-Randall braneworld. In this paper, we fill this gap. We mainly focus on the case that the ambient space is (2+1)-dimensional for which explicit computations can be done in each description of the set-up. We show that the topological phase transition of the Ryu-Takayanagi surface corresponds to the formation of the replica wormhole on the Karch-Randall brane as the dominant contribution to the replica path integral. For higher dimensional situations, we show that the geometry of the brane satisfies Einstein’s equation coupled with conformal matter. We comment on possible implications to the general rule of gravitational path integral from this equation.https://doi.org/10.1007/JHEP01(2025)063AdS-CFT CorrespondenceBlack Holes1/N Expansion |
| spellingShingle | Hao Geng Replica wormholes and entanglement islands in the Karch-Randall braneworld Journal of High Energy Physics AdS-CFT Correspondence Black Holes 1/N Expansion |
| title | Replica wormholes and entanglement islands in the Karch-Randall braneworld |
| title_full | Replica wormholes and entanglement islands in the Karch-Randall braneworld |
| title_fullStr | Replica wormholes and entanglement islands in the Karch-Randall braneworld |
| title_full_unstemmed | Replica wormholes and entanglement islands in the Karch-Randall braneworld |
| title_short | Replica wormholes and entanglement islands in the Karch-Randall braneworld |
| title_sort | replica wormholes and entanglement islands in the karch randall braneworld |
| topic | AdS-CFT Correspondence Black Holes 1/N Expansion |
| url | https://doi.org/10.1007/JHEP01(2025)063 |
| work_keys_str_mv | AT haogeng replicawormholesandentanglementislandsinthekarchrandallbraneworld |