Fayet-Iliopoulos Terms in Supergravity and Cosmology

TL;DR

This work clarifies the structure of 4D N=1 supergravity with constant Fayet--Iliopoulos terms, showing that FI terms induce nonzero R-charges for fermions and the superpotential and mandating a careful revision of D-term inflation in supergravity. It develops the superconformal origin of FI terms, analyzes the rigid limit, and derives the corrected bosonic action including order $gξ/M_P^2$ contributions, while addressing anomaly cancellation and effective field removal. The paper then studies D-term strings, their zero modes, and the consistency of a D-term–D-brane correspondence, including the impact of axion shifts and stabilization of moduli, with implications for cosmology such as inflation dynamics and cosmic strings. It also scrutinizes field-dependent FI terms arising from anomalous U(1)s and the Green–Schwarz mechanism, highlighting the need to stabilize dilaton/volume moduli to render such models cosmologically viable. Collectively, the results bridge 4D supergravity with string-theoretic constructions, delineating when FI terms can yield consistent, observable cosmological scenarios and what moduli-stabilization challenges must be overcome.

Abstract

We clarify the structure of N=1 supergravity in 1+3 dimensions with constant FI terms. The FI terms induce non-vanishing R-charges for the fermions and the superpotential. Therefore the D-term inflation model in supergravity with constant FI terms has to be revisited. We also investigate the case of the so-called anomalous U(1) when a chiral superfield is shifted under U(1). In such a case, in the context of string theory, the FI terms originate from the derivative of the Kaehler potential and they are inevitably field-dependent. This raises an issue of stabilization of the relevant field in applications to cosmology. The recently suggested equivalence between the D-term strings and D-branes of type II theory shows that brane-anti-brane systems produce FI terms in the effective 4d theory, with the Ramond-Ramond axion shifting under the U(1) symmetry. This connection gives the possibility to interpret many unknown properties of D-\bar{D} systems in the more familiar language of 4d supergravity D-terms, and vice versa. For instance, the shift of the axion field in both cases restricts the possible forms of the moduli-stabilizing superpotential. We provide some additional consistency checks of the correspondence of D-term-strings to D-branes and show that instabilities of the two are closely related. Surviving cosmic D-strings of type II theory may be potentially observed in the form of D-term strings of 4d supergravity.