On the Inconsistency of Fayet-Iliopoulos Terms in Supergravity Theories

TL;DR

This paper investigates the consistency of Fayet-Iliopoulos terms in supergravity theories, analyzing their implications on R-symmetry and supercurrent structures across different supergravity formulations.

Contribution

It clarifies the conditions under which Fayet-Iliopoulos terms can be consistently incorporated into supergravity, highlighting the incompatibility issues and differences between formulations.

Findings

Certain Fayet-Iliopoulos contributions to supercurrents do not exist.

Inconsistencies arise from R-symmetry constraints in supergravity.

Differences are identified between chiral and linear supergravity formulations.

Abstract

Motivated by recent discussions, we revisit the issue of whether globally supersymmetric theories with non-zero 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 non-zero 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 non-zero Fayet-Iliopoulos terms.