Physics Letters B 752 (2016) 263–266
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Minimal scalar-less matter-coupled supergravity
Gianguido Dall’Agata
a,b,c,∗
, Sergio Ferrara
d,e,f
, Fabio Zwirner
a,b,d
a
Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy
b
INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
c
Centre de Physique Théorique, École Polytechnique, CNRS, Université Paris-Saclay, F-91128 Palaiseau, France
d
Theory Unit, Physics Department, CERN, CH-1211 Geneva 23, Switzerland
e
INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati, Italy
f
Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
28 September 2015
Accepted
25 November 2015
Available
online 27 November 2015
Editor:
N. Lambert
We build the minimal supergravity model where the nilpotent chiral goldstino superfield is coupled to
a chiral matter superfield, realising a different non-linear representation through a mixed nilpotency
constraint. The model describes the spontaneous breaking of local supersymmetry in the presence of a
generically massive Majorana fermion, but in the absence of elementary scalars. The sign and the size
of the cosmological constant, the spectrum and the four-fermion interactions are controlled by suitable
parameters.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Recently there has been some progress in the embedding of
non-linear realisations of N = 1, D = 4 supersymmetry in super-
gravity,
spontaneously broken through the super-Higgs mechanism
[1,2]. A simple way to implement non-linear realisations is the use
of constrained superfields. The simplest example is the Volkov–
Akulov
realisation [3], which can be obtained by imposing a nilpo-
tency
constraint X
2
= 0on the chiral superfield X containing the
goldstino [4]. Its coupling to supergravity has been recently worked
out, both in the superfield formalism [5,6] and in components [7].
Within supergravity, the couplings of the nilpotent goldstino chi-
ral
superfield to unconstrained matter chiral superfields have also
been considered in [8–11], and some of their properties have been
studied. The most important feature of these models is the replace-
ment
of the elementary complex scalar of the goldstino multiplet,
the sgoldstino [12], with a goldstino bilinear, and this makes them
attractive to build simple semi-realistic models of inflation (for a
recent review and references, see e.g. [13]). However, the elemen-
tary
complex scalars of the unconstrained matter chiral superfields
still belong to the physical spectrum.
In
this letter we address, in supergravity, the coupling of the
goldstino multiplet X ≡ (x, χ, F
x
), obeying the constraint X
2
= 0,
to a matter chiral multiplet Y ≡ ( y, ψ, F
y
), also described by a
*
Corresponding author.
E-mail
address: dallagat@pd.infn.it (G. Dall’Agata).
non-linear representation. As anticipated in the conclusions of [8],
this can be obtained by a mixed nilpotency constraint XY = 0, as
originally introduced in [14] and later extended to a more general
context [15] in global supersymmetry. This constraint removes also
the elementary complex scalar of the Y multiplet from the spec-
trum,
replacing it with a suitable fermion bilinear, but keeps the
spin-1/2 fermion (and the auxiliary field) of Y . We can then call
this model the minimal scalar-less matter-coupled supergravity.
The superspace action we propose is the coupling to supergrav-
ity
of a slightly generalised form of the action in [15]. Namely, we
keep the minimal canonical Kähler potential,
K =|X|
2
+|Y |
2
, (1)
but we introduce the most general superpotential compatible with
the superfield constraints imposed on X and Y :
W = W
0
+ fX+ gY+hY
2
, (2)
where it is not restrictive to assume that (W
0
, f , g) are real, with
f = 0, and for simplicity we also take h to be real.
We
will derive the main physical properties of this minimal
model without writing down the full component action. After solv-
ing
the nilpotency constraints, the scalar potential will just be a
(cosmological) constant,
V
0
≡ V
|
x=y=0
= f
2
+ g
2
−3W
2
0
, (3)
with arbitrary sign or vanishing. For simplicity, we will con-
sider
spontaneous supersymmetry breaking in flat space, V
0
= 0,
http://dx.doi.org/10.1016/j.physletb.2015.11.066
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.