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1We thank Gia Dvali for raising this point. See for instance the
last entry in [21]In a remarkable recent work, Komargodski and Seiberg
[27] have presented a new formalism to understand super-
symmetry breaking, its general properties, its non-linear
realizations [28], and a systematic way to understand the
low-energy couplings of goldstinos to other elds. Al-
though many things were known before (see references in
[27]) this work, the presentation is quite insightful, and it
played a major part in the inspiration of this work.
The basic starting point in [27] is the Ferrara-Zumino
multiplets of currents [29]. A vector super eld composed
of the R-symmetry current, the supercurrent, and the en-
ergy momentum tensor. This vector super eld satis es the
general relation:
D_ J ;_ =D X: (1)
The chiral super eld Xis essentially de ned uniquely2
in the ultraviolet. Following [27] the super eld Xhas the
following properties:
In the UV description of the theory, it appears in the
right hand side of 1, where it represents a measure of
the violation of conformal invariance.
The expectation value of its 2component is the or-
der parameter of supersymmetry breaking. In this
work we are only considering F-breaking of super-
symmetry. We denote by fthe expectation value of
theF-component of X. It will sometimes be useful
to writef=2, whereis the microscopic scale of
supersymmetry breaking.
When supersymmetry is spontaneously broken, we
can follow the
ow of Xto the infrared (IR). In the IR
this eld satis es a non-linear constraint and becomes
2The ambiguities in the supercurrent multiplet and Xare related
to improvement terms in the various currents.
2the \goldstino" super eld3.
X2
NL= 0; (2)
XNL=G2
2F+p
2G+2F: (3)
The scalar component xofXbecomes a goldstino
bilinear. Its fermionic component is the goldstino
fermionG, andFis the auxiliary eld that gets the
vacuum expectation value. A major part in the anal-
ysis in [27] is based on this novel nonlinear constraint
satis ed by the super eld Xin the IR. As shown
there, the correct normalization of the goldstino su-
per eld to derive all relevant low-energy theorems of
broken supersymmetry is XNL=3
8fX.
Finally,Xgeneralizes the usual spurion couplings ap-
pearing in the description of low-energy supersymmet-
ric lagrangians. If msoftdescribes the soft supersym-
metry breaking masses at low energies, the standard
spurion in the lagrangian is replaced bymsoft
fXNL.
This allows one to write the leading low-energy cou-
plings of the goldtino to other matter elds.
Since we are going to consider goldstino couplings, we will
work with a eld whose expectation values are well below
the Planck scale.
Our proposal is to identify in the UV the in
aton eld
with the scalar component of the super eld X. SinceXis
de ned uniquely (up to the ambiguity mentioned in foot-
note one) in the UV, this provides a well de ned prescrip-
tion. Furthermore, we will identify the in
ationary period
precisely with the
ow of Xfrom the UV to the IR i.e.
X!XNL. Note that by making this assumption we do
not need to think of the in
aton as any extra fundamental
eld. In fact, independently of how SUSY is broken, and
3A modi ed version of the nonlinear constraint (2) appears when
one considers spontaneous R-symmetry breaking. In that case, the
goldstino and the corresponding axion will be part of the same mul-
tiplet.what is the underlying fundamental theory we can always
identify the Xsuper eld as well as its scalar component
x. More importantly, by making this assumption we are
identifying the vacuum energy driven in
ation with the
actual SUSY breaking order parameter.
In the supergravity context, once we have the K ahler
potentialK(X;X) and the superpotential W(X), the full
scalar potential is given by [30]:
V=eK
M2(K1
X;XDW DW3
M2jWj2) (4)
with
DW =@XW+1
M2@XKW: (5)
Mis the high energy scale below which we can write the ef-
fective action describing the dynamics of the X-super eld.
It could be the Planck scale, or a GUT scale depending on
the microscopic theory. We will work well below the scale
M, and for simplicity take M=MplIn equation (4) we
can see one of the basic problems in supergravity in
a-