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<p>We study the Hilbert space structure of gauge-invariant operators emergent in large-<i>N</i> 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 <i>q</i>-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.</p>

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Hilbert space of finite N multi-matrix models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月24日

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  • Robert de Mello Koch,
  • Antal Jevicki

摘要

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.