  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.
