The principal chiral field in two dimensions on classical lie algebras: The Bethe-ansatz solution and factorized theory of scattering

Abstract

The Bethe-ansatz solution, the exact factorized complete S-matrix and the particle spectrum for a two-dimensional chiral field on principal manifolds associated with the classical Lie groups SU( k + 1), SO(2 k), SO(2 k + 1), Sp(2 k) are presented. It is shown that the elementary particles are massive and form the basis of the ring of representations of the diagonal of the direct product G × G. The exact results are obtained in the framework of both the Bethe-ansatz approach and the factorized bootstrap program. The bootstrap properties of the S-matrices and relations between the simple roots of the algebras and the solution are discussed.