Supersymmetric σ-models and graded Lie groups (original) (raw)

A geometrical treatment of supersymmetric a-models of ordinary and graded manifolds in given. The action is written in terms of differential forms on superspace, by means of a modified version of the Berezin duality operation. The linear sets associated to the models are explicitly exhibited and the ((reduction , > problem is discussed. 1.-Introduction. Recently a certain amount of interest has been devoted to supersymmetric generalizations of nonlinear a-models. Important results have been obtained by the study of On and CP~ supersymmetric a-models (1) both at the classical and at the quantum level. Moreover, a general treatment of supersymmetric models on Kghler manifolds (3) has been given and supersymmetrie generalizations of principal chirul (3) and symmetric space (4) a-models have been thoroughly discussed. In all these cases the models are obtained by graduation of the two-dimensional space-time, (*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.