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

TL;DR

This paper derives an exact formula for the mass-gap of the supersymmetric O(N) sigma model in two dimensions, confirming the S-matrix's accuracy in reproducing key physical properties and resolving longstanding ambiguities.

Contribution

It provides the first exact mass-gap formula for the supersymmetric O(N) sigma model, validating the S-matrix approach and clarifying CDD ambiguity issues.

Findings

Derived an exact mass-gap formula for N>4

Confirmed the S-matrix reproduces the universal beta-function

Resolved CDD ambiguity problems in the model

Abstract

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