THE S-MATRIX COUPLING DEPENDENCE FOR A-AFFINE, D-AFFINE AND E-AFFINE TODA FIELD-THEORY

Affine Toda field theories are solvable 1 + 1 dimensional quantum field theories closely related to integrable deformations of conformal field theory. The S-matrix elements for an affine Toda field theory are believed to depend on the coupling constant-beta through one universal function B(beta) which cannot be determined by unitarity, crossing and the bootstrap. From the requirement of nonexistence of extra poles in the physical region its form is conjectured to be B(beta) = (2-pi)-1 beta-2/(1 + beta-2/4-pi). We show that the above conjecture is correct up to one-loop order (i.e., beta-4) of perturbation for simply laced, i.e., a, d and e affine Toda field theories using a general argument which exhibits much of the richness of these theories.