566 research outputs found
Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications
We study the behaviour of the string loop corrections to the N=1 4D
supergravity Kaehler potential that occur in flux compactifications of IIB
string theory on general Calabi-Yau three-folds. We give a low energy
interpretation for the conjecture of Berg, Haack and Pajer for the form of the
loop corrections to the Kaehler potential. We check the consistency of this
interpretation in several examples. We show that for arbitrary Calabi-Yaus, the
leading contribution of these corrections to the scalar potential is always
vanishing, giving an "extended no-scale structure". This result holds as long
as the corrections are homogeneous functions of degree -2 in the 2-cycle
volumes. We use the Coleman-Weinberg potential to motivate this cancellation
from the viewpoint of low-energy field theory. Finally we give a simple formula
for the 1-loop correction to the scalar potential in terms of the tree-level
Kaehler metric and the correction to the Kaehler potential. We illustrate our
ideas with several examples. A companion paper will use these results in the
study of Kaehler moduli stabilisation.Comment: 34 pages and 3 figures; typos corrected and references adde
Axionic D3-D7 Inflation
We study the motion of a D3 brane moving within a Type IIB string vacuum
compactified to 4D on K3 x T_2/Z_2 in the presence of D7 and O7 planes. We work
within the effective 4D supergravity describing how the mobile D3 interacts
with the lightest bulk moduli of the compactification, including the effects of
modulus-stabilizing fluxes. We seek inflationary solutions to the resulting
equations, performing our search numerically in order to avoid resorting to
approximate parameterizations of the low-energy potential. We consider
uplifting from D-terms and from the supersymmetry-breaking effects of anti-D3
branes. We find examples of slow-roll inflation (with anti-brane uplifting)
with the mobile D3 moving along the toroidal directions, falling towards a
D7-O7 stack starting from the antipodal point. The inflaton turns out to be a
linear combination of the brane position and the axionic partner of the K3
volume modulus, and the similarity of the potential along the inflaton
direction with that of racetrack inflation leads to the prediction n_s \le 0.95
for the spectral index. The slow roll is insensitive to most of the features of
the effective superpotential, and requires a one-in-10^4 tuning to ensure that
the torus is close to square in shape. We also consider D-term inflation with
the D3 close to the attractive D7, but find that for a broad (but not
exhaustive) class of parameters the conditions for slow roll tend to
destabilize the bulk moduli. In contrast to the axionic case, the best
inflationary example of this kind requires the delicate adjustment of potential
parameters (much more than the part-per-mille level), and gives inflation only
at an inflection point of the potential (and so suffers from additional
fine-tuning of initial conditions to avoid an overshoot problem).Comment: 29 pages, 5 figure
Fibre Inflation: Observable Gravity Waves from IIB String Compactifications
We introduce a simple string model of inflation, in which the inflaton field
can take trans-Planckian values while driving a period of slow-roll inflation.
This leads naturally to a realisation of large field inflation, inasmuch as the
inflationary epoch is well described by the single-field scalar potential . Remarkably, for a broad class of vacua
all adjustable parameters enter only through the overall coefficient , and
in particular do not enter into the slow-roll parameters. Consequently these
are determined purely by the number of \e-foldings, , and so are not
independent: . This implies similar
relations among observables like the primordial scalar-to-tensor amplitude,
, and the scalar spectral tilt, : . is
itself more model-dependent since it depends partly on the post-inflationary
reheat history. In a simple reheating scenario a reheating temperature of
GeV gives , corresponding to and , within reach of future observations. The model is
an example of a class that arises naturally in the context of type IIB string
compactifications with large-volume moduli stabilisation, and takes advantage
of the generic existence there of Kahler moduli whose dominant appearance in
the scalar potential arises from string loop corrections to the Kahler
potential. The inflaton field is a combination of Kahler moduli of a K3-fibered
Calabi-Yau manifold. We believe there are likely to be a great number of models
in this class -- `high-fibre models' -- in which the inflaton starts off far
enough up the fibre to produce observably large primordial gravity waves.Comment: Extended calculations beyond the leading approximations, including
numerical integrations of multi-field evolution; Display an example with ; Simplify the discussion of large fields; Corrected minor errors and
typos; Added references; 41 pages LaTeX, 25 figure
Systematics of Moduli Stabilization, Inflationary Dynamics and Power Spectrum
We study the scalar sector of type IIB superstring theory compactified on
Calabi-Yau orientifolds as a place to find a mechanism of inflation in the
early universe. In the large volume limit, one can stabilize the moduli in
stages using perturbative method. We relate the systematics of moduli
stabilization with methods to reduce the number of possible inflatons, which in
turn lead to a simpler inflation analysis. Calculating the order-of-magnitude
of terms in the equation of motion, we show that the methods are in fact valid.
We then give the examples where these methods are used in the literature. We
also show that there are effects of non-inflaton scalar fields on the scalar
power spectrum. For one of the two methods, these effects can be observed with
the current precision in experiments, while for the other method, the effects
might never be observable.Comment: 20 pages, JHEP style; v.2 and v.3: typos fixed, discussion and
references adde
Sculpting the Extra Dimensions: Inflation from Codimension-2 Brane Back-reaction
We construct an inflationary model in 6D supergravity that is based on
explicit time-dependent solutions to the full higher-dimensional field
equations, back-reacting to the presence of a 4D inflaton rolling on a
space-filling codimension-2 source brane. Fluxes in the bulk stabilize all
moduli except the `breathing' modulus (that is generically present in
higher-dimensional supergravities). Back-reaction to the inflaton roll causes
the 4D Einstein-frame on-brane geometry to expand, a(t) ~ t^p, as well as
exciting the breathing mode and causing the two off-brane dimensions to expand,
r(t) ~ t^q. The model evades the general no-go theorems precluding 4D de Sitter
solutions, since adjustments to the brane-localized inflaton potential allow
the power p to be dialed to be arbitrarily large, with the 4D geometry becoming
de Sitter in the limit p -> infinity (in which case q = 0). Slow-roll solutions
give accelerated expansion with p large but finite, and q = 1/2. Because the
extra dimensions expand during inflation, the present-day 6D gravity scale can
be much smaller than it was when primordial fluctuations were generated -
potentially allowing TeV gravity now to be consistent with the much higher
gravity scale required at horizon-exit for observable primordial gravity waves.
Because p >> q, the 4 on-brane dimensions expand more quickly than the 2
off-brane ones, providing a framework for understanding why the observed four
dimensions are presently so much larger than the internal two. If uplifted to a
10D framework with 4 dimensions stabilized, the 6D evolution described here
could describe how two of the six extra dimensions evolve to become much larger
than the others, as a consequence of the enormous expansion of the 4 large
dimensions we can see.Comment: 27 pages + appendices, 2 figure
Volume Stabilization and the Origin of the Inflaton Shift Symmetry in String Theory
The main problem of inflation in string theory is finding the models with a
flat potential, consistent with stabilization of the volume of the compactified
space. This can be achieved in the theories where the potential has (an
approximate) shift symmetry in the inflaton direction. We will identify a class
of models where the shift symmetry uniquely follows from the underlying
mathematical structure of the theory. It is related to the symmetry properties
of the corresponding coset space and the period matrix of special geometry,
which shows how the gauge coupling depends on the volume and the position of
the branes. In particular, for type IIB string theory on K3xT^2/Z with D3 or D7
moduli belonging to vector multiplets, the shift symmetry is a part of
SO(2,2+n) symmetry of the coset space [SU(1,1)/ U(1)]x[SO(2,2+n)/(SO(2)x
SO(2+n)]. The absence of a prepotential, specific for the stringy version of
supergravity, plays a prominent role in this construction, which may provide a
viable mechanism for the accelerated expansion and inflation in the early
universe.Comment: 12 page
Scanning the Landscape of Flux Compactifications: Vacuum Structure and Soft Supersymmetry Breaking
We scan the landscape of flux compactifications for the Calabi-Yau manifold
with two K\" ahler moduli by varying the value of
the flux superpotential over a large range of values. We do not include
uplift terms. We find a rich phase structure of AdS and dS vacua. Starting with
we reproduce the exponentially large volume scenario, but as
is reduced new classes of minima appear. One of them corresponds to the
supersymmetric KKLT vacuum while the other is a new, deeper non-supersymmetric
minimum. We study how the bare cosmological constant and the soft supersymmetry
breaking parameters for matter on D7 branes depend on , for these classes
of minima. We discuss potential applications of our results.Comment: draft format remove
Kahler Moduli Inflation
We show that under general conditions there is at least one natural
inflationary direction for the Kahler moduli of type IIB flux
compactifications. This requires a Calabi-Yau which has h^{2,1}>h^{1,1}>2 and
for which the structure of the scalar potential is as in the recently found
exponentially large volume compactifications. We also need - although these
conditions may be relaxed - at least one Kahler modulus whose only
non-vanishing triple-intersection is with itself and which appears by itself in
the non-perturbative superpotential. Slow-roll inflation then occurs without a
fine tuning of parameters, evading the eta problem of F-term inflation. In
order to obtain COBE-normalised density perturbations, the stabilised volume of
the Calabi-Yau must be O(10^5-10^7) in string units, and the inflationary scale
M_{infl} ~ 10^{13} GeV. We find a robust model independent prediction for the
spectral index of 1 - 2/N_e = 0.960 - 0.967, depending on the number of
efoldings.Comment: 17 pages, 1 figure; v2. references adde
Metastable SUSY Breaking, de Sitter Moduli Stabilisation and K\"ahler Moduli Inflation
We study the influence of anomalous U(1) symmetries and their associated
D-terms on the vacuum structure of global field theories once they are coupled
to N=1 supergravity and in the context of string compactifications with moduli
stabilisation. In particular, we focus on a IIB string motivated construction
of the ISS scenario and examine the influence of one additional U(1) symmetry
on the vacuum structure. We point out that in the simplest one-Kahler modulus
compactification, the original ISS vacuum gets generically destabilised by a
runaway behaviour of the potential in the modulus direction. In more general
compactifications with several Kahler moduli, we find a novel realisation of
the LARGE volume scenario with D-term uplifting to de Sitter space and both
D-term and F-term supersymmetry breaking. The structure of soft supersymmetry
breaking terms is determined in the preferred scenario where the standard model
cycle is not stabilised non-perturbatively and found to be flavour universal.
Our scenario also provides a purely supersymmetric realisation of Kahler moduli
(blow-up and fibre) inflation, with similar observational properties as the
original proposals but without the need to include an extra (non-SUSY)
uplifting term.Comment: 38 pages, 8 figures. v2: references added, minor correction
Natural Quintessence in String Theory
We introduce a natural model of quintessence in string theory where the light
rolling scalar is radiatively stable and couples to Standard Model matter with
weaker-than- Planckian strength. The model is embedded in an anisotropic type
IIB compactification with two exponentially large extra dimensions and
TeV-scale gravity. The bulk turns out to be nearly supersymmetric since the
scale of the gravitino mass is of the order of the observed value of the
cosmological constant. The quintessence field is a modulus parameterising the
size of an internal four-cycle which naturally develops a potential of the
order (gravitino mass)^4, leading to a small dark energy scale without tunings.
The mass of the quintessence field is also radiatively stable since it is
protected by supersymmetry in the bulk. Moreover, this light scalar couples to
ordinary matter via its mixing with the volume mode. Due to the fact that the
quintessence field is a flat direction at leading order, this mixing is very
small, resulting in a suppressed coupling to Standard Model particles which
avoids stringent fifth-force constraints. On the other hand, if dark matter is
realised in terms of Kaluza-Klein states, unsuppressed couplings between dark
energy and dark matter can emerge, leading to a scenario of coupled
quintessence within string theory. We study the dynamics of quintessence in our
set-up, showing that its main features make it compatible with observations.Comment: 26 page
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