Highlights in Supergravity: CCJ 47 Years Later

TL;DR

This paper revisits the supercurrent in N=1 supergravity, clarifying its formulation via a chiral compensator and exploring its conservation laws in different matter couplings within curved superspace.

Contribution

It provides a detailed expression for the supercurrent in superconformal supergravity and analyzes its conservation laws for various matter couplings in curved superspace.

Findings

Supercurrent expressed via chiral compensator in superconformal formulation

Different conservation laws for superconformal and non-superconformal matter

Application to classifying rigid curved superspace geometries

Abstract

We consider an expression for the supercurrent in the superconformal formulation of N=1 supergravity. A chiral compensator provides the supersymmetric formulation of the Callan-Coleman-Jackiw (CCJ) improved stress energy tensor, when the conformal gauge is used. Superconformal and non-superconformal matter give different conservation laws of the supercurrent, when coupled to the curvature supermultiplets which underlie the local superspace geometry. This approach can be applied to any set of auxiliary fields and it is useful to classify rigid curved superspace geometries. Examples with four supersymmetries are briefly described.