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

Abstract

A formula for the mass-gap of the supersymmetric CP n−1 sigma model ( n > 1) in two dimensions is derived: m Λ MS = sin ( πΔ) (πΔ ) where Δ = 1 n 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.