Hilbert Space of Finite $N$ Multi-matrix Models
Abstract
We study the Hilbert space structure of gauge-invariant operators emergent in large- 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 -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.
Cite
@article{arxiv.2508.11986,
title = {Hilbert Space of Finite $N$ Multi-matrix Models},
author = {Robert de Mello Koch and Antal Jevicki},
journal= {arXiv preprint arXiv:2508.11986},
year = {2025}
}
Comments
1+40 pages