On Global Symmetries and Fayet-Iliopoulos Terms

We revisit the genuine Fayet-Iliopoulos terms of 4D N=1 supergravity. Such terms are commonly believed to preserve a global symmetry, and therefore they are in conflict with the principles of quantum gravity. However, we find that generically there do exist supersymmetric terms that break explicitly the specific global symmetry, while preserving gauge invariance. We illustrate this, by providing a series of examples, including superpotentials and superspace higher order terms, along with a general prescription for their construction.