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arXiv · 2507.09454

Relationship between a $\Phi^4$ matrix model and harmonic oscillator systems

Harald Grosse·Naoyuki Kanomata·Akifumi Sako·Raimar Wulkenhaar
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Abstract

A Hermitian $\Phi^4$ matrix model with a Kontsevich-type kinetic term is studied. It was recently discovered that the partition function of this matrix model satisfies the Schr\"odinger equation of the $N$-body harmonic oscillator, and that eigenstates of the Virasoro operators can be derived from this partition function. We extend these results and obtain an explicit formula for such eigenstates in terms of the free energy. Furthermore, the Schr\"odinger equation for the $N$-body harmonic oscillator can also be reformulated in terms of connected correlation functions. The $U(1)^N$-symmetry allows us to derive loop equations.

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Harald Grosse, Naoyuki Kanomata, Akifumi Sako, Raimar Wulkenhaar. 2025-07-13. Relationship between a $\Phi^4$ matrix model and harmonic oscillator systems. https://arxiv.org/abs/2507.09454

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