The exact mass-gaps of the principal chiral models

Abstract

An exact expression for the mass-gap, the ratio of the physical particle mass to the $\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.

11 pages, (macro included), CERN-TH.7164/94, SWAT/93-94/26

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