Physics Letters B 781 (2018) 723–727
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Taking a vector supermultiplet apart: Alternative Fayet–Iliopoulos-type
terms
Sergei M. Kuzenko
Department of Physics M013, The University of Western Australia, 35 Stirling Highway, Crawley, W.A. 6009, Australia
a r t i c l e i n f o a b s t r a c t
Article history:
Received
20 February 2018
Accepted
24 April 2018
Available
online 27 April 2018
Editor:
M. Cveti
ˇ
c
Starting from an Abelian N = 1vector supermultiplet V coupled to conformal supergravity, we construct
from it a nilpotent real scalar Goldstino superfield V of the type proposed in arXiv:1702 .02423. It
contains only two independent component fields, the Goldstino and the auxiliary D-field. The important
properties of this Goldstino superfield are: (i) it is gauge invariant; and (ii) it is super-Weyl invariant.
As a result, the gauge prepotential can be represented as V = V + V, where V contains only one
independent component field, modulo gauge degrees of freedom, which is the gauge one-form. Making
use of V allows us to introduce new Fayet–Iliopoulos-type terms, which differ from the one proposed in
arXiv:1712 .08601 and share with the latter the property that gauged R-symmetry is not required.
© 2018 The Author. 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
In quantum field theory with a symmetry group G sponta-
neously
broken to its subgroup H, the multiplet of matter fields
transforming according to a linear representation of G can be split
into two subsets: (i) the massless Goldstone fields; and (ii) the
other fields that are massive in general. Each subset transforms
nonlinearly with respect to G and linearly under H. Each sub-
set
may be realised in terms of constrained fields transforming
linearly under G [1,2]. In the case of spontaneously broken super-
symmetry
[3], every superfield U containing the Goldstino may be
split into two supermultiplets, one of which is an irreducible Gold-
stino
superfield
1
and the other contains the remaining component
fields [4], in accordance with the general relation between linear
and nonlinear realisations of N = 1 supersymmetry [5]. It is worth
recalling the example worked out in [4]. Consider the irreducible
chiral Goldstino superfield X ,
¯
D
˙
α
X = 0, introduced in [5,6]. It is
defined to obey the constraints [6]
X
2
= 0 , f X =−
1
4
X
¯
D
2
¯
X , (1.1)
E-mail address: sergei .kuzenko @uwa .edu .au.
1
The notion of irreducible and reducible Goldstino superfields was introduced in
[4]. For every irreducible Goldstino superfield, the Goldstino is its only independent
component. Reducible Goldstino superfields also contain auxiliary field(s) in addi-
tion
to the Goldstino.
where f is a real parameter characterising the scale of supersym-
metry
breaking. As U we choose the reducible chiral Goldstino
superfield X ,
¯
D
˙
α
X = 0, proposed in [7,8]. It is subject only to the
constraint
X
2
= 0 . (1.2)
It was shown in [4] that X can be represented in the form
X = X + Y , f X := −
1
4
¯
D
2
(
¯
), := −4 f
¯
X
¯
D
2
¯
X
, (1.3)
where the auxiliary field F of X is the only independent com-
ponent
of the chiral scalar Y . Originally, the irreducible Goldstino
superfield was introduced in [9]to be a modified complex linear
superfield, −
1
4
¯
D
2
= f , which is nilpotent and obeys a holomor-
phic
nonlinear constraint,
2
= 0 , fD
α
=−
1
4
¯
D
2
D
α
. (1.4)
These properties follow from (1.3).
The
approach advocated in [4]may be pursued one step fur-
ther
with the goal to split any unconstrained superfield U into two
supermultiplets, one of which is a reducible Goldstino supermul-
tiplet.
This has been implemented in [10]for the reducible chiral
Goldstino superfield X . There exist two other reducible Goldstino
superfields: (i) the three-form variant of X [11,12]; and (ii) the
nilpotent real scalar superfield introduced in [13]. In the present
https://doi.org/10.1016/j.physletb.2018.04.051
0370-2693/
© 2018 The Author. 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
.
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