Collective field theory of the matrix-vector models

Abstract

We construct collective field theories associated with one-matrix plus r vector models. Such field theories describe the continuum limit of spin Calogero-Moser models. The invariant collective fields consist of a scalar density coupled to a set of fields in the adjoint representation of U( r). Hermiticity conditions for the general quadratic Hamiltonians lead to a new type of extended non-linear algebra of differential operators acting on the Jacobian. It includes both Virasoro and SU( r) (included in sl(r, C) × sl(r, C)) current algebras. A systematic construction of exact eigenstates for the coupled field theory is given and exemplified.