Integrable theories that are asymptotically CFT

TL;DR

This paper studies sigma models with torsion that generate mass dynamically and have non-trivial conformal fixed points, confirming their integrability through S-matrix analysis and thermodynamic methods.

Contribution

It provides evidence for the quantum integrability of these models by testing the proposed S-matrix against perturbative and thermodynamic calculations.

Findings

Confirmation of integrability via S-matrix and Thermodynamic Bethe Ansatz

Universal coefficients of the beta-function derived

Mass gap evaluated to leading order in 1/k

Abstract

A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; this is confirmed by postulating a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-function and allows for an evaluation of the mass gap (the ratio of the physical mass to the $\Lambda$-parameter) to leading order in $1/k$.