On Fayet-Iliopoulos terms and de Sitter vacua in supergravity: some easy pieces

TL;DR

This paper clarifies the role of Fayet-Iliopoulos terms in supergravity, showing when they are genuine or can be redefined away, and constructs a model with a stable de Sitter vacuum without global symmetries.

Contribution

It provides a minimal formalism explanation for FI terms, introduces an anomaly-free model with a genuine FI term and stable dS vacuum, and discusses N=2 to N=1 FI term relations.

Findings

FI terms are not genuine if the U(1) vector is massive everywhere.

A simple anomaly-free model with a genuine FI term and stable de Sitter vacuum is formulated.

The relation between N=2 and N=1 FI terms is explored through truncations.

Abstract

We clarify a number of issues on Fayet-Iliopoulos (FI) terms in supergravity, keeping the formalism at a minumum and making use of explicit examples. We explain why, if the U(1) vector is massive everywhere in field space, FI terms are not genuine and can always be redefined away or introduced when they are not present. We formulate a simple anomaly-free model with a genuine FI term, a classically stable de Sitter (dS) vacuum and no global symmetries. We explore the relation between N=2 and N=1 FI terms by discussing N=1 truncations of N=2 models with classically stable dS vacua.