Monodromy inflation in SUSY QCD
Michael Dine
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Patrick Draper
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Angelo Monteux
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Santa Cruz Institute for Particle Physics, University of California Santa Cruz
, 1156 High Street, Santa Cruz,
U.S.A
The discovery of a large tensor-to-scalar ratio by the BICEP2 experiment points to large field excursions during inflation. One framework that predicts large r is monodromy inflation. While discussed mainly in the context of string theory, the phenomenon can be illustrated and studied in the well-understood framework of SUSY QCD with a large number of colors. We discuss the requirements for viable inflation as well as various difficulties for model building, including tunneling, tuning, and the species problem.
1 Introduction
3.1 Anomaly-mediated model
3.2 Inflation
3.3 Self-consistency
3.4 Tunings and higher order corrections
3.5 Tunneling 4 Conclusions
Introduction
The BICEP2 discovery [1, 2] of B-modes in the perturbations of the cosmic microwave
background constitutes strong evidence for primordial gravitational waves emitted during
inflation. The large value of the tensor-to-scalar ratio, r = 0.2, provides an interesting
challenge for inflationary model-building. In single-field slow-roll inflation models, a
wellknown argument due to Lyth [3] connects a large amplitude for the tensor perturbations
with transplanckian excursions in field space during inflation. Such models are challenging
to place under theoretical control.
One class of models that already pointed toward inflaton excursions beyond Mpl, and
thus to substantial tensor perturbations, is natural inflation [4] (another is chaotic
inflation [5]). Natural inflation (NI) models rely on an approximate, spontaneously broken
global symmetry to provide a quasi-flat direction, which we refer to as an axion. Successful
inflation, in the simplest version, requires an axion decay constant substantially larger than
Mpl. Such large decay constants are hard to understand in effective field theory,
particularly if quantum gravity breaks the global symmetry explicitly. In string theory (more
generally higher-dimensional theories) compactification on small volumes can appear to
produce such fields [6]. However, by exploiting various dualities, one can show that the
effective decay constants are not parametrically large [7]. An interesting approach to
evading this difficulty is monodromy inflation. Discussed principally in string theory [8, 9],
the basic idea is to consider axions with subplanckian decay constants, fa < Mpl, and
dynamics that permit angular excursions much larger than 2.1 Following the BICEP2
announcement, there have been a number of studies updating and extending earlier work
on natural inflation [15] and monodromy inflation [1621].
1A different approach, involving multiple axionic directions [1014], will not be explored here.
To fully understand monodromy inflation in string models is challenging. For example,
to construct a complete model requires understanding all of the details of moduli fixing; in
general, for example, one expects to find moduli with Hubble scale masses during inflation.
Another potential problem is controlling tunneling between branches. These issues are
typically quite complex.
Monodromy inflation has also been realized in some field theory models [2228]. In
this note we discuss a simple setting for monodromy in a familiar four-dimensional field
theory, supersymmetric QCD (SQCD), where the number of colors is tied to the number
of e-foldings.2 While not necessarily advocating that a large N gauge group at very high
scales describes our universe, such theories provide a theoretically tractable class of toy
inflation models exhibiting the monodromy mechanism. By assumption, for example, there
are no moduli; the potential for the axion is readily calculated, and tunneling issues are
accessible to familiar field theory methods and approximations. We believe some of the
lessons learned here may extend to string theory models, though the details (for example
the precise form of the potential) may not.
In section 2, we briefly discuss globally supersymmetric QCD with a mass term for the
quarks, and show that while it possesses monodromy for an angular field, it does not easily
give large field excursions in that direction unless a separate SUSY-breaking sector is added.
In section 3 we couple the system to supergravity and show that adding a constant to the
superpotential generates, in a manner analogous to anomaly mediation, a natural inflation
potential over O(N ) windings of the angle. Stabilizing the radial direction at subplanckian
values during inflation is achieved by adding soft SUSY-breaking terms to the potential. We
discuss the parameter ranges relevant for inflation and check that the hierarchies required
for the validity of the effective field theory analysis can in principle be satisfied. We will
see that an important shortcoming is the presence of a set of meso-tunings3 in the model.4
Finally, we discuss tunneling processes that (...truncated)