The Graded Differential Geometry of Mixed Symmetry Tensors

TL;DR

This paper explores the use of $Z_2^n$-manifolds, a generalization of supermanifolds, to provide a geometric framework for mixed symmetry tensors like the dual graviton, applicable to flat and curved spacetimes.

Contribution

It introduces a graded differential geometric approach to mixed symmetry tensors using $Z_2^n$-manifolds, expanding the mathematical tools for their study.

Findings

$Z_2^n$-manifolds offer a new geometric perspective on mixed symmetry tensors.

The approach applies to both flat and curved spacetimes.

Provides a foundation for further geometric and physical investigations.

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.