On supercurrent superfields and Fayet–Iliopoulos terms in image gauge theories Original Research Article

We revisit the supermultiplet structure of Noether currents for image 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 image 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 image-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 image supergravity.