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

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

1994-09-23

arxiv.org/abs/hep-th/9409141v1

Phys.Lett. B343 (1995) 189-197

Physics

High Energy Physics

High Energy Physics - Theory

Plain TeX (macro included), CERN-TH.7426/94, SWAT/93-94/39

Scientific paper

10.1016/0370-2693(94)01477-T

A formula for the mass-gap of the supersymmetric O($N$) sigma model ($N>4$) in two dimensions is derived: $m/\Lambda_{\overline{\rm MS}}=2^{2\Delta}\sin(\pi\Delta)/(\pi\Delta)$, 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.

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