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: m/Lambda(MS)- = 2(2 Delta) Sin(pi De lta)/(pi Delta), where Delta = 1/(N - 2) and m is the mass of the fund amental vector particle in the theory. This result is obtained by comp aring two expressions for the free-energy density in the presence of a coupling to a conserved charge; one expression is computed from the e xact S-matrix of Shankar and Witten via the the thermodynamic Bethe an satz and the other is computed using conventional perturbation theory. These calculations provide a stringent test of the S-matrix, showing that it correctly reproduces the universal part of the beta-function a nd resolving the problem of CDD ambiguities.