Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity

TL;DR

This paper develops a formalism for constructing Chern-Simons actions involving Abelian tensor hierarchies within 4D N=1 supergravity, utilizing conformal superspace to solve constraints and express solutions via prepotentials.

Contribution

It introduces a method to solve field strength constraints and derive transformation laws for p-form gauge superfields in 4D N=1 supergravity with tensor hierarchies.

Findings

Explicit solutions for gauge superfield constraints

Transformation laws for prepotentials

Descent formalism for Chern-Simons actions

Abstract

We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional ${\cal N}=1$ supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the $p$-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the $p$-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.