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