Real symmetric $\Phi^4$-matrix model as Calogero-Moser model

Akifumi Sako; Harald Grosse; Naoyuki Kanomata; Raimar Wulkenhaar

Real symmetric $\Phi^4$-matrix model as Calogero-Moser model

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arxiv 2311.10974 v1 pith:NDNJPJVC submitted 2023-11-18 hep-th math-phmath.MP

Harald Grosse , Naoyuki Kanomata , Akifumi Sako , Raimar Wulkenhaar This is my paper · ORCID

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keywords matrixmodelcalogero-moserfunctionpartitionrealsymmetricalgebra

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abstract

We study a real symmetric $\Phi^4$-matrix model whose kinetic term is given by $\mathrm{Tr}( E \Phi^2)$, where $E$ is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Sch\"odinger type equation with Calogero-Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.

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Relationship between a $\Phi^4$ matrix model and harmonic oscillator systems
hep-th 2025-07 conditional novelty 6.0 of 10

The paper gives a free-energy formula for Virasoro eigenstates and a connected-correlator form of the Schwinger-Dyson equation for the Phi^4 matrix model with Kontsevich-type kinetic term.

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