Charged moments in W 3 higher spin holography
Abstract We consider the charged moments in SL(3, ℝ) higher spin holography, as well as in the dual two-dimensional conformal field theory with W 3 symmetry. For the vacuum state and a single entangling interval, we show that the W 3 algebra of the conformal field theory induces an entanglement W3 a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2022)166 |
| _version_ | 1818213777369202688 |
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| author | Suting Zhao Christian Northe Konstantin Weisenberger René Meyer |
| author_facet | Suting Zhao Christian Northe Konstantin Weisenberger René Meyer |
| author_sort | Suting Zhao |
| collection | DOAJ |
| description | Abstract We consider the charged moments in SL(3, ℝ) higher spin holography, as well as in the dual two-dimensional conformal field theory with W 3 symmetry. For the vacuum state and a single entangling interval, we show that the W 3 algebra of the conformal field theory induces an entanglement W3 algebra acting on the quantum state in the entangling interval. The algebra contains a spin 3 modular charge which commutes with the modular Hamiltonian. The reduced density matrix is characterized by the modular energy and modular charge, hence our definition of the charged moments is also with respect to these conserved quantities. We evaluate the logarithm of the charged moments perturbatively in the spin 3 modular chemical potential, by computing the corresponding connected correlation functions of the modular charge operator up to quartic order in the chemical potential. This method provides access to the charged moments without using charged twist fields. Our result matches known results for the charged moment obtained from the charged topological black hole picture in SL(3, ℝ) higher spin gravity. Since our charged moments are not Gaussian in the chemical potential any longer, we conclude that the dual W 3 conformal field theories must feature breakdown of equipartition of entanglement to leading order in the large c expansion. |
| first_indexed | 2024-12-12T06:09:41Z |
| format | Article |
| id | doaj.art-c3d4e565da684c97a2a2616b545232bb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T06:09:41Z |
| publishDate | 2022-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-c3d4e565da684c97a2a2616b545232bb2022-12-22T00:35:11ZengSpringerOpenJournal of High Energy Physics1029-84792022-05-012022512810.1007/JHEP05(2022)166Charged moments in W 3 higher spin holographySuting Zhao0Christian Northe1Konstantin Weisenberger2René Meyer3Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität WürzburgInstitut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität WürzburgInstitut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität WürzburgInstitut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität WürzburgAbstract We consider the charged moments in SL(3, ℝ) higher spin holography, as well as in the dual two-dimensional conformal field theory with W 3 symmetry. For the vacuum state and a single entangling interval, we show that the W 3 algebra of the conformal field theory induces an entanglement W3 algebra acting on the quantum state in the entangling interval. The algebra contains a spin 3 modular charge which commutes with the modular Hamiltonian. The reduced density matrix is characterized by the modular energy and modular charge, hence our definition of the charged moments is also with respect to these conserved quantities. We evaluate the logarithm of the charged moments perturbatively in the spin 3 modular chemical potential, by computing the corresponding connected correlation functions of the modular charge operator up to quartic order in the chemical potential. This method provides access to the charged moments without using charged twist fields. Our result matches known results for the charged moment obtained from the charged topological black hole picture in SL(3, ℝ) higher spin gravity. Since our charged moments are not Gaussian in the chemical potential any longer, we conclude that the dual W 3 conformal field theories must feature breakdown of equipartition of entanglement to leading order in the large c expansion.https://doi.org/10.1007/JHEP05(2022)166AdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Suting Zhao Christian Northe Konstantin Weisenberger René Meyer Charged moments in W 3 higher spin holography Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | Charged moments in W 3 higher spin holography |
| title_full | Charged moments in W 3 higher spin holography |
| title_fullStr | Charged moments in W 3 higher spin holography |
| title_full_unstemmed | Charged moments in W 3 higher spin holography |
| title_short | Charged moments in W 3 higher spin holography |
| title_sort | charged moments in w 3 higher spin holography |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP05(2022)166 |
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