The exact mass-gaps of the principal chiral models

TL;DR

This paper derives exact mass-gap expressions for principal chiral sigma models linked to classical Lie algebras, validating the scattering matrix through thermodynamic and perturbative methods.

Contribution

It provides the first exact formulas for the mass-gap in these models, confirming the structure of the scattering matrix.

Findings

Exact mass-gap formulas for all classical Lie algebra models

Validation of the scattering matrix structure

Agreement between thermodynamic Bethe Ansatz and perturbation theory

Abstract

An exact expression for the mass-gap, the ratio of the physical particle mass to the $\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.