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: Shota Komatsu, Adrien Martina, Joao Penedones, Noé Suchel, Antoine Vuignier, Xiang Zhao
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP04(2025)169
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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.
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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
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AT antoinevuignier gravityfromquantummechanicsoffinitematrices
AT xiangzhao gravityfromquantummechanicsoffinitematrices