{"title":"Gravity from quantum mechanics of finite matrices","authors":"Shota Komatsu, Adrien Martina, Joao Penedones, Noé Suchel, Antoine Vuignier, Xiang Zhao","doi":"10.1007/JHEP04(2025)169","DOIUrl":null,"url":null,"abstract":"<p>We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of <i>N</i> × <i>N</i> matrices. In particular, we study the BMN MQM at strong coupling and finite <i>N</i> 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.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2025 4","pages":""},"PeriodicalIF":5.5000,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP04(2025)169.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of High Energy Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/JHEP04(2025)169","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal.
Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles.
JHEP presently encompasses the following areas of theoretical and experimental physics:
Collider Physics
Underground and Large Array Physics
Quantum Field Theory
Gauge Field Theories
Symmetries
String and Brane Theory
General Relativity and Gravitation
Supersymmetry
Mathematical Methods of Physics
Mostly Solvable Models
Astroparticles
Statistical Field Theories
Mostly Weak Interactions
Mostly Strong Interactions
Quantum Field Theory (phenomenology)
Strings and Branes
Phenomenological Aspects of Supersymmetry
Mostly Strong Interactions (phenomenology).
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