Collective field theory of the matrix-vector model
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.