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 $R\ge 3$ 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.

Extensive modifications in the construction of the spinon basis and the subsequent computations of eigenvalues and eigenvectors. Title and references modified. To appear in Nuclear Physics B. 21 pages, Latex

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