Field Theories on Supermanifolds: General Formalism, Local Supersymmetry, and the Limit of Global Supersymmetry

Abstract

The aim of this paper is to report briefly on recent investigations concerning the formulation of field theories on supermanifolds. The motivation of this research is twofold. On one hand, the usual formulations of “superspace field theories”, see e.g. Ref.1, are highly unsatisfactory from a mathematical viewpoint. The main criticisms that can be aroused are: (i) in classical (non-quantum) supersymmetric field theories spinor components have to be anticommuting c-numbers (?); (ii) superspace2 is defined formally (for instance, general coordinate transformations are mathematically not well defined). As a consequence, there is no room for studying global (topological) properties of superspace; (iii) most manipulations (e.g. the derivation of field equations from a variational principle) are merely formal.