On Global Symmetries and Fayet-Iliopoulos Terms

TL;DR

This paper examines the nature of Fayet-Iliopoulos terms in 4D N=1 supergravity, revealing that they can explicitly break global symmetries while maintaining gauge invariance, challenging common beliefs.

Contribution

It demonstrates that supersymmetric Fayet-Iliopoulos terms can break global symmetries explicitly, providing examples and a general construction method.

Findings

Fayet-Iliopoulos terms can break global symmetries explicitly

Explicit symmetry breaking occurs while preserving gauge invariance

Provides a construction prescription for such terms

Abstract

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.