Hilbert space of finite N multi-matrix models

A bstract We study the Hilbert space structure of gauge-invariant operators emergent in large- N multi-matrix quantum mechanics. Building on the framework of 1, 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.