Inflation with Fayet-Iliopoulos Terms

TL;DR

The paper analyzes how Fayet-Iliopoulos terms drive inflation in supergravity, contrasting constant FI terms (D-term hybrid inflation and potential chaotic inflation post-waterfall) with field-dependent FI terms arising from a Green-Schwarz anomalous U(1) and a stabilized modulus. It demonstrates that, when the FI term is field-dependent and the modulus participates, modulus stabilization and inflation become intrinsically coupled, challenging simple D-term inflation realizations. The authors show that a clean DHI can be difficult to achieve in UV completions, but a string-inspired F-term approach can recover chaotic inflation after integrating out heavy fields, with the modulus mass controlled by the FI term and potentially decoupled if it sits above the Hubble scale. A simple toy model illustrates how modulus stabilization and a heavy vector can yield an effective single-field chaotic inflation theory, supporting scenarios where moduli do not participate in SUSY breaking. Overall, the work clarifies the UV viability of FI-term-based inflation and highlights when modulus dynamics must be accounted for in multi-field inflation models.

Abstract

Two of the most attractive realizations of inflation in supergravity are based upon the presence of a constant Fayet-Iliopoulos (FI) term. In D-term hybrid inflation it is the FI term itself which sets the energy scale of inflation. Alternatively, the breaking of a U(1) symmetry induced by the FI term can dynamically generate the quadratic potential of chaotic inflation. The purpose of this note is to study the possible UV embedding of these schemes in terms of the `field-dependent FI term' related to a string modulus field which is stabilized by a non-perturbative superpotential. We find that in settings where the FI term drives inflation, gauge invariance prevents a decoupling of the modulus from the inflationary dynamics. The resulting inflation models generically contain additional dynamical degrees of freedom compared to D-term hybrid inflation. However, the dynamical realization of chaotic inflation can be obtained in complete analogy to the case of a constant FI term. We present a simple string-inspired toy model of this type.