Fayet–Iliopoulos terms in supergravity and D-term inflation
Eur. Phys. J. C
Fayet-Iliopoulos terms in supergravity and D-term inflation
I. Antoniadis 1 2
A. Chatrabhuti 0
H. Isono 0
R. Knoops 0
0 Department of Physics, Faculty of Science, Chulalongkorn University , Phayathai Road, Pathumwan, Bangkok 10330 , Thailand
1 Albert Einstein Center, Institute for Theoretical Physics, University of Bern , Sidlerstrasse 5, 3012 Bern , Switzerland
2 Laboratoire de Physique Théorique et Hautes Energies - LPTHE, Sorbonne Université , CNRS, 4 Place Jussieu, 75005 Paris , France
We analyse the consequences of a new gauge invariant Fayet-Iliopoulos (FI) term proposed recently to a class of inflation models driven by supersymmetry breaking with the inflaton being the superpartner of the goldstino. We first show that charged matter fields can be consistently added with the new term, as well as the standard FI term in supergravity in a Kähler frame where the U (1) is not an Rsymmetry. We then show that the slow-roll conditions can be easily satisfied with inflation driven by a D-term depending on the two FI parameters. Inflation starts at initial conditions around the maximum of the potential where the U (1) symmetry is restored and stops when the inflaton rolls down to the minimum describing the present phase of our Universe. The resulting tensor-to-scalar ratio of primordial perturbations can be even at observable values in the presence of higher order terms in the Kähler potential.
1 Introduction
In a recent work [1], we proposed a class of minimal
inflation models in supergravity that solve the η-problem in a
natural way by identifying the inflaton with the goldstino
superpartner in the presence of a gauged R-symmetry. The
goldstino/inflaton superfield has then charge one, the
superpotential is linear and the scalar potential has a maximum
at the origin with a curvature fixed by the quartic correction
to the Kähler potential K expanded around the symmetric
point. The D-term has a constant Fayet–Iliopoulos (FI)
contribution but plays no role in inflation and can be neglected,
while the pseudoscalar partner of the inflaton is absorbed by
the U (
1
)R gauge field that becomes massive away from the
origin.
Recently, a new FI term was proposed [2] that has three
important properties: (
1
) it is manifestly gauge invariant
already at the Lagrangian level; (
2
) it is associated to a U (
1
)
that should not gauge an R-symmetry and (
3
)
supersymmetry is broken by (at least) a D-auxiliary expectation value and
the extra bosonic part of the action is reduced in the unitary
gauge to a constant FI contribution leading to a positive shift
of the scalar potential, in the absence of matter fields. In the
presence of neutral matter fields, the FI contribution to the
Dterm acquires a special field dependence e2K /3 that violates
invariance under Kähler transformations.
In this work, we study the properties of the new FI term
and explore its consequences to the class of inflation
models we introduced in [1].1 We first show that matter fields
charged under the U (
1
) gauge symmetry can consistently
be added in the presence of the new FI term, as well as a
non-trivial gauge kinetic function. We then observe that the
new FI term is not invariant under Kähler transformations.
On the other hand, a gauged R-symmetry in ordinary Kähler
invariant supergravity can always be reduced to an ordinary
(non-R) U (
1
) by a Kähler transformation. By then going to
such a frame, we find that the two FI contributions to the
U (
1
) D-term can coexist, leading to a novel contribution to
the scalar potential.
The resulting D-term scalar potential provides an
alternative realisation of inflation from supersymmetry breaking,
driven by a D- instead of an F-term. The inflaton is still a
superpartner of the goldstino which is now a gaugino within
a massive vector multiplet, where again the pseudoscalar
partner is absorbed by the gauge field away from the
origin. For a particular choice of the inflaton charge, the scalar
potential has a maximum at the origin where inflation occurs
and a supersymmetric minimum at zero energy, in the limit
of negligible F-term contribution (such as in the absence of
superpotential). The slow roll conditions are automatically
1 This new FI term was also studied in [3] to remove an instability
from inflation in Polonyi-Starobinsky supergravity.
satisfied near the point where the new FI term cancels the
charge of the inflaton, leading to higher than quadratic
contributions due to its non trivial field dependence.
The Kähler potential can be canonical, modulo the Kähler
transformation that takes it to the non R-symmetry frame.
In the presence of a small superpotential, the inflation is
practically unchanged and driven by the D-term, as before.
However, the maximum is now slightly shifted away from
the origin and the minimum has a small non-vanishing
positive vacuum energy, where supersymmetry is broken by both
F- and D-auxiliary expectation values of similar magnitude (...truncated)