Higher-dimensional Willmore energy as holographic entanglement entropy
Abstract The vacuum entanglement entropy of a general conformal field theory (CFT) in d = 5 spacetime dimensions contains a universal term, F(A), which has a complicated and non-local dependence on the geometric details of the region A and the theory. Analogously to the previously known d = 3 case,...
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| Format: | Article |
| Language: | English |
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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)081 |
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| author | Giorgos Anastasiou Ignacio J. Araya Pablo Bueno Javier Moreno Rodrigo Olea Alejandro Vilar Lopez |
| author_facet | Giorgos Anastasiou Ignacio J. Araya Pablo Bueno Javier Moreno Rodrigo Olea Alejandro Vilar Lopez |
| author_sort | Giorgos Anastasiou |
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| description | Abstract The vacuum entanglement entropy of a general conformal field theory (CFT) in d = 5 spacetime dimensions contains a universal term, F(A), which has a complicated and non-local dependence on the geometric details of the region A and the theory. Analogously to the previously known d = 3 case, we prove that for CFTs in d = 5 which are holographically dual to Einstein gravity, F(A) is equal to a four-dimensional version of the “Willmore energy” associated to a doubled and closed version of the Ryu-Takayanagi (RT) surface of A embedded in ℝ5. This generalized Willmore energy is shown to arise from a conformal-invariant codimension-two functional obtained by evaluating six-dimensional Conformal Gravity on the conically-singular orbifold of the replica trick. The new functional involves an integral over the doubled RT surface of a linear combination of three quartic terms in extrinsic curvatures and is free from ultraviolet divergences by construction. We verify explicitly the validity of our new formula for various entangling regions and argue that, as opposed to the d = 3 case, F(A) is not globally minimized by a round ball A = 𝔹4. Rather, F(A) can take arbitrarily positive and negative values as a function of A. Hence, we conclude that the round ball is not a global minimizer of F(A) for general five-dimensional CFTs. |
| format | Article |
| id | doaj-art-3737403f9a2343f9aec013fce7b48d8a |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
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| spelling | doaj-art-3737403f9a2343f9aec013fce7b48d8a2025-02-09T12:08:17ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025114610.1007/JHEP01(2025)081Higher-dimensional Willmore energy as holographic entanglement entropyGiorgos Anastasiou0Ignacio J. Araya1Pablo Bueno2Javier Moreno3Rodrigo Olea4Alejandro Vilar Lopez5Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo IbañezDepartamento de Física y Astronomía, Facultad de Ciencias Exactas, Universidad Andres BelloDepartament de Física Quántica i Astrofísica, Institut de Ciéncies del Cosmos, Universitat de BarcelonaDepartament de Física Quántica i Astrofísica, Institut de Ciéncies del Cosmos, Universitat de BarcelonaInstituto de Física, Pontificia Universidad Católica de ValparaísoPhysique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles (ULB)Abstract The vacuum entanglement entropy of a general conformal field theory (CFT) in d = 5 spacetime dimensions contains a universal term, F(A), which has a complicated and non-local dependence on the geometric details of the region A and the theory. Analogously to the previously known d = 3 case, we prove that for CFTs in d = 5 which are holographically dual to Einstein gravity, F(A) is equal to a four-dimensional version of the “Willmore energy” associated to a doubled and closed version of the Ryu-Takayanagi (RT) surface of A embedded in ℝ5. This generalized Willmore energy is shown to arise from a conformal-invariant codimension-two functional obtained by evaluating six-dimensional Conformal Gravity on the conically-singular orbifold of the replica trick. The new functional involves an integral over the doubled RT surface of a linear combination of three quartic terms in extrinsic curvatures and is free from ultraviolet divergences by construction. We verify explicitly the validity of our new formula for various entangling regions and argue that, as opposed to the d = 3 case, F(A) is not globally minimized by a round ball A = 𝔹4. Rather, F(A) can take arbitrarily positive and negative values as a function of A. Hence, we conclude that the round ball is not a global minimizer of F(A) for general five-dimensional CFTs.https://doi.org/10.1007/JHEP01(2025)081AdS-CFT CorrespondenceField Theories in Higher DimensionsRenormalization and Regularization |
| spellingShingle | Giorgos Anastasiou Ignacio J. Araya Pablo Bueno Javier Moreno Rodrigo Olea Alejandro Vilar Lopez Higher-dimensional Willmore energy as holographic entanglement entropy Journal of High Energy Physics AdS-CFT Correspondence Field Theories in Higher Dimensions Renormalization and Regularization |
| title | Higher-dimensional Willmore energy as holographic entanglement entropy |
| title_full | Higher-dimensional Willmore energy as holographic entanglement entropy |
| title_fullStr | Higher-dimensional Willmore energy as holographic entanglement entropy |
| title_full_unstemmed | Higher-dimensional Willmore energy as holographic entanglement entropy |
| title_short | Higher-dimensional Willmore energy as holographic entanglement entropy |
| title_sort | higher dimensional willmore energy as holographic entanglement entropy |
| topic | AdS-CFT Correspondence Field Theories in Higher Dimensions Renormalization and Regularization |
| url | https://doi.org/10.1007/JHEP01(2025)081 |
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