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

TL;DR

This paper derives an exact formula for the mass-gap in the supersymmetric CP^{n-1} sigma model, validating the S-matrix approach and resolving ambiguities through a comparison of free-energy calculations.

Contribution

It provides the first exact mass-gap formula for the supersymmetric CP^{n-1} sigma model, confirming the S-matrix's correctness and addressing CDD ambiguity issues.

Findings

Derived the exact mass-gap formula involving sine function

Validated the S-matrix against perturbative results

Resolved CDD ambiguity problems in the S-matrix

Abstract

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