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arXiv · 2508.11986

Hilbert Space of Finite $N$ Multi-matrix Models

Robert de Mello Koch·Antal Jevicki
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Abstract

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 na\"ive semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories.

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Robert de Mello Koch, Antal Jevicki. 2025-08-16. Hilbert Space of Finite $N$ Multi-matrix Models. https://arxiv.org/abs/2508.11986

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