The Exact Mass-Gap of the Supersymmetric O(N) Sigma Model

Abstract

A formula for the mass-gap of the supersymmetric O($N$) sigma model ($N>4$) in two dimensions is derived: $m/{\Lambda }_{\overline{\mathrm{MS}}}=2^{2\Delta }\sin (\pi \Delta )/(\pi \Delta )$, where $\Delta =1/(N-2)$ 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 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/93-94/39

References in corpus (1)

• The exact mass-gaps of the principal chiral models

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