Hilbert Space of Finite $N$ Multi-matrix Models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912539821998080 |
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| author | Koch, Robert de Mello Jevicki, Antal |
| author_facet | Koch, Robert de Mello Jevicki, Antal |
| contents | We study the Hilbert space structure of gauge-invariant operators emergent in large-$N$ multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we identify a class of light single-trace operators that behave like free creation operators at low energy but saturate beyond a critical excitation level, ceasing to generate new states. This $q$-reducibility is a direct consequence of finite N trace identities and leads to a dramatic truncation of the high-energy spectrum of the emergent theory. The resulting number of independent degrees of freedom is far smaller than naïve semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert Space of Finite $N$ Multi-matrix Models Koch, Robert de Mello Jevicki, Antal High Energy Physics - Theory We study the Hilbert space structure of gauge-invariant operators emergent in large-$N$ multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we identify a class of light single-trace operators that behave like free creation operators at low energy but saturate beyond a critical excitation level, ceasing to generate new states. This $q$-reducibility is a direct consequence of finite N trace identities and leads to a dramatic truncation of the high-energy spectrum of the emergent theory. The resulting number of independent degrees of freedom is far smaller than naïve semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories. |
| title | Hilbert Space of Finite $N$ Multi-matrix Models |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.11986 |