Superforms in Five-Dimensional, $N = 1$ Superspace

TL;DR

This paper explores the structure of superforms in five-dimensional N=1 superspace, revealing new features like branching, fusion, and a gap in the complex, and relating it to six-dimensional superspace through dimensional reduction.

Contribution

It explicitly constructs the five-dimensional super-de Rham complex, introduces a new notion of dimensional reduction, and uncovers novel features such as super-cocycles and a gap in the complex.

Findings

Discovery of branching and fusion in the super-de Rham complex

Identification of a gap in the complex for D > 4 with superconformal parameters

Introduction of a new notion of dimensional reduction relating 5D and 6D superspaces

Abstract

We examine the five-dimensional super-de Rham complex with $N = 1$ supersymmetry. The elements of this complex are presented explicitly and related to those of the six-dimensional complex in $N = (1, 0)$ superspace through a specific notion of dimensional reduction. This reduction also gives rise to a second source of five-dimensional super-cocycles that is based on the relative cohomology of the two superspaces. In the process of investigating these complices, we discover various new features including branching and fusion (loops) in the super-de Rham complex, a natural interpretation of "Weil triviality", $p$-cocycles that are not supersymmetric versions of closed bosonic $p$-forms, and the opening of a "gap" in the complex for $D > 4$ in which we find a multiplet of superconformal gauge parameters.