Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

Abstract

A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special role. As an application of the classification, it is shown that a particular class of these models is on-shell ultraviolet finite to all orders in perturbation theory. © 1981 Springer-Verlag.