Purely elastic scattering theories and their ultraviolet limits

We use the thermodynamic Bethe ansatz to find the finite-size corrections to the ground-state energy in an arbitrary (1+1)-dimensional purely elastic scattering theory. The leading finite-size effects are characterized by tilde c=c-12d0, where c and d0 are the central charge and the lowest scaling dimension, respectively, of the (possibly nonunitary) CFT describing the ultraviolet limit of the massive scattering theory. After presenting the purely elastic S-matrix theories that emerged in recent discussions of perturbed CFTs, we calculate their finite-size scaling coefficient tilde c. Our results show that the UV limits of the 'minimal' S-matrix theories are the unperturbed CFTs in question. On the other hand, the S-matrices which have been suggested to describe affine Toda field theories, differing from the minimal S-matrices by coupling-dependent factors, are seen to have free bosonic CFTs as their UV limits. We also discuss some interesting properties of tilde c. In particular, we suggest that tilde c is a measure of the number of degrees of freedom of an arbitrary two-dimensional CFT. (orig.)