THE EXACT MASS-GAPS OF THE PRINCIPAL CHIRAL MODELS

An exact expression for the mass-gap, the ratio of the physical partic le mass to the LAMBDA-parameter, is found for the principal chiral sig ma models associated to all the classical Lie algebras. The calculatio n is based on a comparison of the free-energy in the presence of a sou rce coupling to a conserved charge of the theory computed in two ways: via the Thermodynamic Bethe Ansatz from the exact scattering matrix a nd directly in perturbation theory. The calculation provides a non-tri vial test of the form of the exact scattering matrix.