Yangian-invariant field theory of matrix-vector models

Abstract

We extend our study of the field-theoretic description of matrix-vector models and the associated many-body problems of one dimensional particles with spin. We construct their Yangian- su( R) invariant Hamiltonian. It describes an interacting theory of a c = 1 collective boson and a k = 1 su( R) current algebra. When R ⩾ 3 cubic-current terms arise. Their coupling is determined by the requirement of the Yangian symmetry. The Hamiltonian can be consistently reduced to finite-dimensional subspaces of states, enabling an explicit computation of the spectrum which we illustrate in the simplest case.