Virasoro entanglement Berry phases
Abstract We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism on the circle: one that diagonalizes the adjoint action of the modular Hamiltonian. These v...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2022)179 |
| _version_ | 1828914241121288192 |
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| author | Jan de Boer Ricardo Espíndola Bahman Najian Dimitrios Patramanis Jeremy van der Heijden Claire Zukowski |
| author_facet | Jan de Boer Ricardo Espíndola Bahman Najian Dimitrios Patramanis Jeremy van der Heijden Claire Zukowski |
| author_sort | Jan de Boer |
| collection | DOAJ |
| description | Abstract We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism on the circle: one that diagonalizes the adjoint action of the modular Hamiltonian. These vector fields exhibit kinks at the interval boundary, thus together with their central extension they differ from usual elements of the Virasoro algebra. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which differs appreciably from known Virasoro orbits. We find that the boundary parallel transport process computes a bulk symplectic form for a Euclidean geometry obtained from the backreaction of a cosmic brane, with Dirichlet boundary conditions at the location of the brane. We propose that this gives a reasonable definition for the symplectic form on an entanglement wedge. |
| first_indexed | 2024-12-13T19:50:44Z |
| format | Article |
| id | doaj.art-906326fdcff045528a2efb181f93d0e9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T19:50:44Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-906326fdcff045528a2efb181f93d0e92022-12-21T23:33:25ZengSpringerOpenJournal of High Energy Physics1029-84792022-03-012022314910.1007/JHEP03(2022)179Virasoro entanglement Berry phasesJan de Boer0Ricardo Espíndola1Bahman Najian2Dimitrios Patramanis3Jeremy van der Heijden4Claire Zukowski5Institute for Theoretical Physics, University of AmsterdamInstitute for Theoretical Physics, University of AmsterdamInstitute for Theoretical Physics, University of AmsterdamFaculty of Physics, University of WarsawInstitute for Theoretical Physics, University of AmsterdamInstitute for Theoretical Physics, University of AmsterdamAbstract We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism on the circle: one that diagonalizes the adjoint action of the modular Hamiltonian. These vector fields exhibit kinks at the interval boundary, thus together with their central extension they differ from usual elements of the Virasoro algebra. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which differs appreciably from known Virasoro orbits. We find that the boundary parallel transport process computes a bulk symplectic form for a Euclidean geometry obtained from the backreaction of a cosmic brane, with Dirichlet boundary conditions at the location of the brane. We propose that this gives a reasonable definition for the symplectic form on an entanglement wedge.https://doi.org/10.1007/JHEP03(2022)179AdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Jan de Boer Ricardo Espíndola Bahman Najian Dimitrios Patramanis Jeremy van der Heijden Claire Zukowski Virasoro entanglement Berry phases Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | Virasoro entanglement Berry phases |
| title_full | Virasoro entanglement Berry phases |
| title_fullStr | Virasoro entanglement Berry phases |
| title_full_unstemmed | Virasoro entanglement Berry phases |
| title_short | Virasoro entanglement Berry phases |
| title_sort | virasoro entanglement berry phases |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP03(2022)179 |
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