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 are presented. In a suitable dilatational gauge, \tthe 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.
Highlights
In the superconformal formalism of supergravity, which is a very practical and economic way for an off-shell formulation, the Planck mass mp = κ−1 = 2.4 × 1018 GeV emerges as a consequence of the superconformal gauge fixing of a chiral multiplet compensator X0
It has been relevant to consider the difference between two gauge choices for dilatations, which correspond to Einstein gauge and ‘conformal gauge’
The conformal case is characterized by a homogeneity of Φ(S, S) + 3 of order 1 both in S and S, and of the superpotential W (S), which should be homogenous order 3
Summary
Since the latter satisfies a similar conservation equation [3], which includes the chiral scalar curvature R, Dα ̇ Eαα = DαR ,. We will construct the full non-linear Einstein tensor from field equations of pure supergravity. The latter is constructed as the D-action of the compensating multiplet X0 (see notations in appendix A). The entire supergravity geometry is encoded in the Einstein tensor Ea, the chiral scalar curvature R and the Weyl superfield Wαβγ. In appendix E we present the Poincare form of the Einstein tensor multiplet
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