The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model

Abstract

A formula for the mass-gap of the supersymmetric $\CP^{n-1}$ sigma model ($n>1$) in two dimensions is derived: $m/{\Lambda }_{\overline{\mathrm{MS}}}=\sin (\pi \Delta )/(\pi \Delta )$ where $\Delta =1/n$ 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.

Plain TeX (macro included), CERN-TH.7426/94, SWAT/93-94/42

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