The exact mass-gap of the supersymmetric O(N) sigma model

A formula for the mass-gap of the supersymmetric O(N) sigma model (N > 4) in two dimensions is derived: mΛMS=22Δsin(πΔ)(πΔ), where Δ = 1(N−2) and m is the mass of the fundamental vector particle in the theory. This result is obtained by comparing two expressions for the free-energy density in the presence of a coupling to a conserved charge; one expression is computed from the exact S-matrix of Shankar and Witten via the thermodynamic Bethe ansatz and the other is computed using conventional perturbation theory. These calculations a provide a stringent test of the S-maxtrix, showing that it correctly reproduces the universal part of the beta-functional and resolving the problem of CDD ambiguities.