INTEGRABLE THEORIES THAT ARE ASYMPTOTICALLY CFT

A series of sigma models with torsion are analysed which generate thei r mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories - in fact SU(2) WZW models at level k. In co ntrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered her e may be termed ''asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; this is confirmed by postu lating a factorizable S-matrix to describe their infra-red behaviour a nd then carrying out a stringent test of this proposal. The test invol ves coupling the theory to a conserved charge and evaluating the respo nse of the free-energy both in perturbation theory to one loop and dir ectly from the S-matrix via the Thermodynamic Bethe Ansatz with a chem ical potential at zero temperature. Comparison of these results provid es convincing evidence in favour of the proposed S-matrix; it also yie lds the universal coefficients of the beta-function and allows for an evaluation of the mass gap (the ratio of the physical mass to the Lamb da-parameter) to leading order in 1/k.