Abelian tensor hierarchy in 4D ${\cal N}=1$ conformal supergravity

TL;DR

This paper develops a formalism for Abelian tensor hierarchies in 4D ${ m N}=1$ supergravity using conformal superspace, expressing form fields via gauge-invariant superfields and connecting superspace with superconformal tensor calculus.

Contribution

It introduces a covariant superspace approach to Abelian tensor hierarchies in 4D ${ m N}=1$ supergravity, providing explicit solutions to Bianchi identities and linking different formalisms.

Findings

Superfields for form fields are explicitly constructed.

The superform action is formulated with invariant superfields.

The relation between superspace and superconformal tensor calculus is clarified.

Abstract

We consider Abelian tensor hierarchy in four-dimensional ${\cal N}=1$ supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce $p$-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the superforms. As a result, each of form fields is expressed by a single gauge invariant superfield. The action of superforms is shown with the invariant superfields. We also show the relation between the superspace formalism and the superconformal tensor calculus.