On AdS$_4$ superspace and supergravity

TL;DR

This paper explores the structure of AdS$_4$ superspace and supergravity, introducing new linear representations of supersymmetry and reformulating the supergravity action in a covariant manner.

Contribution

It constructs novel linear superspace representations, including the superspinor and supervector, and reformulates AdS$_4$ supergravity in a manifestly supersymmetric framework.

Findings

New linear superspace representations are developed.

The supergravity action is expressed in a covariant form.

Fermionic coordinates form a faithful non-linear representation.

Abstract

In the $N=1$ superspace, AdS$_4$ supersymmetry is realized as the non-linear super coordinate transformations. The fermionic coordinates form a faithful non-linear representation of supersymmetry on their own. By introducing an auxiliary scalar coordinate, this representation is reformulated as a 5-dimensional linear representation, i.e., the superspinor representation. New linear representations are constructed by tensor products of multiple superspinors. Especially, the superspace bosonic coordinates are embedded in the supervector representation, which is the traceless symmetric part of the bi-superspinor representation. Based on these linear representations, the $N=1$ AdS$_4$ supergravity action can be reproduced in a manifestly supersymmetry-covariant way.