Real symmetric Φ^4-matrix model as Calogero-Moser model

Grosse, Harald; Kanomata, Naoyuki; Sako, Akifumi; Wulkenhaar, Raimar

Abstract

We study a real symmetric Φ4-matrix model whose kinetic term is given by Tr(EΦ2), 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.