The Supercurrent and Einstein equations in the Superconformal formulation

Abstract

We give a new expression for the supercurrent and its conservation in curved $\mathcal{N}=1$, $D=4$ superspace using the superconformal approach. The first component of the superfield, whose lowest component is the vector auxiliary field gives the (super)Einstein equations. Its trace and couplings to conformal and non-conformal matter is presented. In a suitable dilatational gauge, the conformal gauge, we obtain an update of the Callan-Coleman-Jackiw improved currents for conformal matter, containing $R$-symmetry corrections for a new traceless covariantly conserved energy--momentum tensor. We observe that in the Poincaré gauge, where standard Poincaré supergravity is usually formulated, the currents are not improved and then the higher conformal symmetry of the matter sector is obscured. The curvature multiplets are used to find supersymmetric curved backgrounds and some examples are exhibited in agreement with existing results.

43 pages; v2: Typos corrected. A subsection, an appendix and references added

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• Non-linear Realizations and Higher Curvature Supergravity
• Non-linear realisations in global and local supersymmetry
• Comments on Nonlinear Sigma Models Coupled to Supergravity
• Highlights in Supergravity: CCJ 47 Years Later
• Comments on rigid and local supercurrents in $\mathcal{N}=1$ minimal Supergravity
• Noether Supercurrents, Supergravity and Broken Supersymmetry