On the Inconsistency of Fayet-Iliopoulos Terms in Supergravity Theories

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.

Comments: 69 pages, LaTeX, 2 figures, 7 tables. Significant new material on conformal-compensator formalisms added, previous results clarified and extended, references added

References in corpus (3)

• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• Continuous Global Symmetries and Hyperweak Interactions in String Compactifications
• Anomaly Cancellation in Supergravity with Fayet-Iliopoulos Couplings

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