EXACT S-MATRIX AND PERTURBATIVE CALCULATIONS IN AFFINE TODA THEORIES BASED ON LIE-SUPERALGEBRAS

We determine exact S-matrices for affine Toda theories based on the Lie superalgebras A(2)(0,2n - 1) and C(2)(n + 1). These theories may be viewed as generalizations of the bosonic Toda theories based on the nonsimply laced algebras a2n - 1(2) and c(n)(1), but contain fermions whose presence evidently restores the integrability properties the bosonic theories lose at the quantum level. We verify that the S-matrices we obtain are consistent with the tree-level amplitudes computed from the corresponding lagrangians, and that the second-order poles they contain are explained by contributions from one-loop diagrams.