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

Abstract

AbstractWe study a real symmetric $$\Phi ^4$$ Φ 4 -matrix model whose kinetic term is given by $$\textrm{Tr}( E \Phi ^2)$$ Tr ( E Φ 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 Schrödinger type equation with Calogero–Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.