Abelian Tensor Hierarchy in 4D, N=1 Superspace

TL;DR

This paper develops a superspace formalism for Abelian tensor hierarchies in 4D, N=1 supersymmetry, enabling the construction of supersymmetric actions and higher-dimensional Chern-Simons forms from compactified theories.

Contribution

It introduces a novel embedding of the Abelian tensor hierarchy into 4D, N=1 superspace, facilitating the derivation of supersymmetric invariants and higher-dimensional Chern-Simons forms.

Findings

Constructed supersymmetric Chern-Simons-like invariants in 4D, N=1 superspace.

Derived the eleven-dimensional Chern-Simons form using four-dimensional superfields.

Provided a formalism connecting higher-dimensional theories with 4D supersymmetric actions.

Abstract

With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.