The exact mass-gap of the supersymmetric CPn−1 sigma model

A formula for the mass-gap of the supersymmetric CPn−1 sigma model (n > 1) in two dimensions is derived: mΛMS = sin (πΔ)(πΔ) where Δ = 1n and m is the mass of the fundamental particle multiplet. 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 Köberle and Kurak via the thermodynamic Bethe ansatz 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 and resolving the problem of CDD ambiguities.