Physics Letters B 742 (2015) 390–393
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Chaotic inflation from nonlinear sigma models in supergravity
Simeon Hellerman
a
, John Kehayias
a,b,∗
, Tsutomu T. Yanagida
a
a
Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8582,
Japan
b
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, United States
a r t i c l e i n f o a b s t r a c t
Article history:
Received
13 January 2015
Accepted
7 February 2015
Available
online 11 February 2015
Editor:
J. Hisano
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a
shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the
Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB) of a nonlinear
sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler
transformations are problematic to couple to supergravity. An additional field is necessary to make the
Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry — making
it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space
SU(3)/SU(2) × U(1), with the Higgs as the NGB, including breaking the inflaton’s shift symmetry and
producing a chaotic inflation potential. This construction can also be applied to other models, such as
one based on E
7
/SO(10) × U(1) × U (1) which incorporates the first two generations of (light) quarks as
the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify
and connect previous work on understanding NLSMs in supergravity and the origin of the extra field
(which is the inflaton here), including a connection to Witten–Bagger quantization. This framework has
wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the
structure for chaotic inflaton or an axion.
© 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 and motivation
Over the past two years there have been several exciting ex-
perimental
results, which both confirm theories developed long
before as well as challenge us to better understand their origin.
The discovery of the Higgs boson [1] brings renewed attention to
the issue of the apparent lightness of the Higgs mass compared to
any UV scale, like the Planck mass. The Higgs is not the only light
field we are puzzled over; the lightness (smallness of the Yukawa
couplings) of the first two generations of quarks is a longstand-
ing
question. More recently, there has been much discussion on
the possible discovery of B-modes in the CMB by BICEP2 [2], but
which may be due to dust [3] rather than primordial gravitational
waves. However, a large value for the tensor to scalar ratio, r ∼0.1,
is still possible. Such a value, or more generally any motivations of
models for high scale or large field inflation like chaotic inflation
[4], raises the question of how to control higher dimensional op-
*
Corresponding author.
E-mail
addresses: simeon.hellerman.1@gmail.com (S. Hellerman),
john.kehayias@vanderbilt.edu (J. Kehayias), tsutomu.tyanagida@ipmu.jp
(T.T. Yanagida).
erators which will not be suppressed in the inflaton potential. In
these models, where do such large field values (of order or greater
than the Planck scale) come from, and how are such models con-
sistent?
There
are several ways to address these problems, although it
is not at all obvious that they could be closely related. Consider
first the Higgs mass, which can be generated by a supersymmet-
ric
mass term. One requires some way to either generate a mass
much smaller than the supersymmetry scale, or else forbid this op-
erator.
If the Higgs is a Nambu–Goldstone boson (NGB) of a G/H
nonlinear
sigma model (NLSM) [5], this would do both of these
things: a NGB is massless at first approximation, and cannot have
such a mass term. The Higgs mass is then protected until we in-
troduce
operators which break G/H . More generally, we can think
of any light particle, such as the first two generations of quarks, as
a possible NGB (or fermion partner under supersymmetry) from a
NLSM.
However,
as soon as we consider local supersymmetry, we run
into well known problems for coupling a NLSM to supergravity [6].
The reason is that the Kähler potential has a nontrivial transforma-
tion,
K (,
†
) → K (,
†
) + g() + g
†
(
†
), (1)
http://dx.doi.org/10.1016/j.physletb.2015.02.019
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
.
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