Explicit large $N$ von Neumann algebras from matrix models
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916479650234368 |
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| author | Gesteau, Elliott Santilli, Leonardo |
| author_facet | Gesteau, Elliott Santilli, Leonardo |
| contents | We construct a large family of quantum mechanical systems that give rise to an emergent type III$_1$ von Neumann algebra in the large $N$ limit. Their partition functions are matrix integrals that appear in the study of various gauge theories. We calculate the real-time, finite temperature correlation functions in these systems and show that they are described by an emergent type III$_1$ von Neumann algebra at large $N$. The spectral density underlying this algebra is computed in closed form in terms of the eigenvalue density of a discrete matrix model. Furthermore, we explain how to systematically promote these theories to systems with a Hagedorn transition, and show that a type III$_1$ algebra only emerges above the Hagedorn temperature. Finally, we empirically observe in examples a correspondence between the space of states of the quantum mechanics and Calabi--Yau manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit large $N$ von Neumann algebras from matrix models Gesteau, Elliott Santilli, Leonardo High Energy Physics - Theory Mathematical Physics Operator Algebras Quantum Physics We construct a large family of quantum mechanical systems that give rise to an emergent type III$_1$ von Neumann algebra in the large $N$ limit. Their partition functions are matrix integrals that appear in the study of various gauge theories. We calculate the real-time, finite temperature correlation functions in these systems and show that they are described by an emergent type III$_1$ von Neumann algebra at large $N$. The spectral density underlying this algebra is computed in closed form in terms of the eigenvalue density of a discrete matrix model. Furthermore, we explain how to systematically promote these theories to systems with a Hagedorn transition, and show that a type III$_1$ algebra only emerges above the Hagedorn temperature. Finally, we empirically observe in examples a correspondence between the space of states of the quantum mechanics and Calabi--Yau manifolds. |
| title | Explicit large $N$ von Neumann algebras from matrix models |
| topic | High Energy Physics - Theory Mathematical Physics Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2402.10262 |