Integrable N=2 supersymmetric field theories

Abstract A classification is given of Toda-like theories with N = 2 supersymmetry which are integrable by virtue of some underlying Lie superalgebra. In addition to the N = 2 superconformal theories based on sl( m , m −1), which generalize the Liouville model, a family of massive N = 2 theories based on the algebras sl( m , m ) (1) is found, providing natural generalizations of the sine-Gordon theory. A third family of models based on sl( m , m ) which have global supersymmetry, a version of conformal invariance, but no superconformal invariance is also briefly discussed. Unlike their N = 0 and N = 1 cousins, the N = 2 massive theories apparently cannot be directly thought of as integrable deformations of the corresponding N = 2 superconformal theories. It is shown that these massive theories admit supersymmetric soliton solutions and a form for their exact S -matrices is conjectured.