Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace

TL;DR

This paper develops a superspace formulation of non-abelian tensor hierarchies and Chern-Simons actions in 4D, N=1 supersymmetry, including their cohomological gauge invariance and dimensional reduction from higher-dimensional theories.

Contribution

It introduces superfield analogs for tensor fields and constructs supersymmetric Chern-Simons actions with a cohomological gauge invariance framework.

Findings

Constructed superfield versions of tensor hierarchies

Developed supersymmetric Chern-Simons actions

Connected structures to dimensional reduction from 11D supergravity

Abstract

We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield analogs for the tensor fields, along with covariant superfield strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1 cases, and note that the condition of gauge invariance can be presented cohomologically. Finally, we provide an explicit realization of these structures by dimensional reduction, for example by reducing the three-form of eleven-dimensional supergravity into a superspace with manifest 4D, N=1 supersymmetry.