The Graded Differential Geometry of Mixed Symmetry Tensors

Abstract

We show how the theory of ${\mathbb{Z}}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

9 pages. Several changes as compared with earlier versions. In particular, we have added "supersymmetries" of mixed symmetry tensors and have included a section on mixed symmetry tensors with values in vector bundles