A global theory of supermanifolds

Abstract

A mathematically rigorous definition of a global supermanifold is given. This forms an appropriate model for a global version of superspace, and a class of functions is defined which corresponds to superfields. This new construction is compared with several pre-existing definitions of supermanifold and graded manifold; it is shown to include all these definitions and to go beyond them, particularly in admitting the possibility of nontrivial topology in the anticommuting sector. Local differential geometry and potential applications to supergravity are considered.