Comments on rigid and local supercurrents in ${\cal N}=1$ minimal Supergravity

TL;DR

This paper examines local supercurrents in ${ m extbf{N}=1}$ minimal supergravity, exploring their role as sources in super-Einstein equations, modifications due to Fayet-Iliopoulos terms, and alternative methods for identifying rigid supersymmetric backgrounds.

Contribution

It provides a detailed analysis of supercurrents in minimal supergravity, including their modifications and applications in curved supersymmetric backgrounds.

Findings

Supercurrents serve as sources in super-Einstein equations.

Fayet-Iliopoulos terms modify Ward identities.

Curvature multiplets offer an alternative to gravitino variations.

Abstract

We discuss local supercurrents as sources of the super-Einstein equations in the superconformal approach in the old and new minimal (auxiliary fields) formulation. Modifications of the Ward identity giving the covariant divergence of the Einstein multiplet are considered in presence of a Fayet-Iliopoulos term. Curvature multiplets can be used as alternative to the gravitino variation in the search for rigid supersymmetric curved backgrounds.