Taking a vector supermultiplet apart: Alternative Fayet-Iliopoulos-type terms

Starting from an Abelian ${\cal N}=1$ vector supermultiplet $V$ coupled to conformal supergravity, we construct from it a nilpotent real scalar Goldstino superfield $\mathfrak V$ of the type proposed in arXiv:1702.02423. It contains only two independent component fields, the Goldstino and the auxiliary $D$-field. The important properties of this Goldstino superfield are: (i) it is gauge invariant; and (ii) it is super-Weyl invariant. As a result, the gauge prepotential can be represented as $V={\cal V} +\mathfrak V$, where $\cal V$ contains only one independent component field, modulo gauge degrees of freedom, which is the gauge one-form. Making use of $\mathfrak V$ allows us to introduce new Fayet-Iliopoulos-type terms, which differ from the one proposed in arXiv:1712.08601 and share with the latter the property that gauged $R$-symmetry is not required.