Comments on the Fayet-Iliopoulos term in field theory and supergravity

A careful analysis of the Fayet-Iliopoulos (FI) model shows that its energy momentum tensor and supersymmetry current are not gauge invariant. Since the corresponding charges are gauge invariant, the model is consistent. However, our observation about the currents gives a new perspective on its restrictive renormalization group flow and explains why FI-terms never appear in dynamical supersymmetry breaking. This lack of gauge invariance is at the root of the complications of coupling the model to supergravity. We show that this is possible only if the full supergravity theory (including all higher derivative corrections) has an additional exact continuous global symmetry. A consistent quantum gravity theory cannot have such symmetries and hence FI-terms cannot appear. Our results have consequences for various models of particle physics and cosmology.