On supercurrent superfields and Fayet–Iliopoulos terms in N=1N=1 gauge theories

We revisit the supermultiplet structure of Noether currents for N=1N=1 supersymmetric gauge theories. Using superfield identities and the field equations we show how to derive a superfield equation for the divergences of the Noether currents in terms of the supercurrent and anomaly superfields containing 16B+16F16B+16F components. We refer to this as the natural supercurrent structure as it is invariant under all local symmetries of the theory. It corresponds to the SS-multiplet of Komargodski and Seiberg. We clarify the on/off-shell nature of the currents appearing in this multiplet and we study in detail the effect of specific improvement transformations leading to (1) a Ferrara–Zumino multiplet and to (2) a multiplet containing the new improved energy–momentum tensor of Callan, Coleman and Jackiw. Our methods also apply to supersymmetric gauge theories with a Fayet–Iliopoulos term. We construct the natural supercurrent multiplet for such a theory and show how to improve this to a formally gauge-invariant Ferrara–Zumino multiplet by introducing a non-dynamical chiral superfield S to ensure superfield gauge invariance. Finally we study the coupling of this theory to supergravity and show that S remains non-dynamical if the theory is R-symmetric and that S becomes propagating if the theory is not R  -symmetric, leading to non-minimal 16B+16F16B+16F supergravity.