Abstract
Recently, a new type of constant Fayet–Iliopoulos (FI) terms was introduced in {mathcal {N}}=1 supergravity, which do not require the gauging of the R-symmetry. We revisit and generalise these constructions, building a new class of Kähler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the U(1) which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.
Highlights
IntroductionAn alternative construction was made in [7] preserving Kähler invariance and leading to a constant FI-term in the presence of matter, that generates a constant uplift of the vacuum energy
The simplest extension of pure N = 1 supergravity in flat spacetime is the anti de Sitter (AdS) supergravity, where a negative cosmological constant is included [1]
We generalised the construction of new FI Dterms in N = 1 supergravity that do not require the gauging of R-symmetry and preserve invariance under ordinary Kähler transformations
Summary
An alternative construction was made in [7] preserving Kähler invariance and leading to a constant FI-term in the presence of matter, that generates a constant uplift of the vacuum energy Such FI-terms were written in N = 2 supergravity exhibiting a much richer structure [8]. We show that there is a region in the parameter space where the resulting scalar potential possesses an inflationary plateau describing successfully the cosmological observations with the inflaton rolling down to a minimum with tuneable vacuum energy, where the gravitino mass and the supersymmetry breaking scale are fixed in terms of the parameters of the model. 2, we review the recent construction of the new FI-term in N = 1 supergravity without gauging the R-symmetry, and its generalisation to a Kähler invariant FI Lagrangian leading to a positive constant uplift of the scalar potential in the presence of arbitrary matter chiral multiplets.
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