On the inconsistency of Fayet-Iliopoulos terms in supergravity theories

Motivated by recent discussions, we revisit the issue of whether globally supersymmetric theories with nonzero Fayet-Iliopoulos terms may be consistently coupled to supergravity. In particular, we examine claims that a fundamental inconsistency arises due to the conflicting requirements which are imposed on the R-symmetry properties of the theory by the supergravity framework. We also prove that certain kinds of Fayet-Iliopoulos contributions to the supercurrent supermultiplets of theories with nonzero Fayet-Iliopoulos terms fail to exist. A key feature of our discussion is an explicit comparison between results from the chiral (or "old minimal") and linear (or "new minimal") formulations of supergravity, and the effects within each of these formalisms that are induced by the presence of nonzero Fayet-Iliopoulos terms.