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 Λ-parameter) to leading
order in 1/k.Comment: typos in two important formulae corrected, references added, version
to appear in Nucl. Phys. B, 21 pages, plain tex with macro include