Gravity from quantum mechanics of finite matrices
Abstract We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of N × N matrices. In particular, we study the BMN MQM at strong coupling and finite N and derive an effective Hamiltonian that describes non-relativisti...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2025)169 |
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| _version_ | 1850277845750775808 |
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| author | Shota Komatsu Adrien Martina Joao Penedones Noé Suchel Antoine Vuignier Xiang Zhao |
| author_facet | Shota Komatsu Adrien Martina Joao Penedones Noé Suchel Antoine Vuignier Xiang Zhao |
| author_sort | Shota Komatsu |
| collection | DOAJ |
| description | Abstract We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of N × N matrices. In particular, we study the BMN MQM at strong coupling and finite N and derive an effective Hamiltonian that describes non-relativistic free particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian matches the supergravity excitation spectrum around the PP-wave background, if we further assume the existence of bound states. Our derivation is based on the strong coupling expansion of the wavefunction and supersedes the naive path integral approach that can lead to incorrect results, as we demonstrate in a simple toy model. We conclude with open questions about various regimes of the theory when we vary the size of the matrices, the coupling and the temperature. |
| format | Article |
| id | doaj-art-e49bbc8bd9ba47c99273bf795f44498b |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e49bbc8bd9ba47c99273bf795f44498b2025-08-20T01:49:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-04-012025416510.1007/JHEP04(2025)169Gravity from quantum mechanics of finite matricesShota Komatsu0Adrien Martina1Joao Penedones2Noé Suchel3Antoine Vuignier4Xiang Zhao5Theoretical Physics Department, CERNFields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Fields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Fields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Fields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Fields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)Abstract We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of N × N matrices. In particular, we study the BMN MQM at strong coupling and finite N and derive an effective Hamiltonian that describes non-relativistic free particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian matches the supergravity excitation spectrum around the PP-wave background, if we further assume the existence of bound states. Our derivation is based on the strong coupling expansion of the wavefunction and supersedes the naive path integral approach that can lead to incorrect results, as we demonstrate in a simple toy model. We conclude with open questions about various regimes of the theory when we vary the size of the matrices, the coupling and the temperature.https://doi.org/10.1007/JHEP04(2025)169Gauge-Gravity CorrespondenceModels of Quantum Gravity |
| spellingShingle | Shota Komatsu Adrien Martina Joao Penedones Noé Suchel Antoine Vuignier Xiang Zhao Gravity from quantum mechanics of finite matrices Journal of High Energy Physics Gauge-Gravity Correspondence Models of Quantum Gravity |
| title | Gravity from quantum mechanics of finite matrices |
| title_full | Gravity from quantum mechanics of finite matrices |
| title_fullStr | Gravity from quantum mechanics of finite matrices |
| title_full_unstemmed | Gravity from quantum mechanics of finite matrices |
| title_short | Gravity from quantum mechanics of finite matrices |
| title_sort | gravity from quantum mechanics of finite matrices |
| topic | Gauge-Gravity Correspondence Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP04(2025)169 |
| work_keys_str_mv | AT shotakomatsu gravityfromquantummechanicsoffinitematrices AT adrienmartina gravityfromquantummechanicsoffinitematrices AT joaopenedones gravityfromquantummechanicsoffinitematrices AT noesuchel gravityfromquantummechanicsoffinitematrices AT antoinevuignier gravityfromquantummechanicsoffinitematrices AT xiangzhao gravityfromquantummechanicsoffinitematrices |