1,247 research outputs found
Minimal Stability in Maximal Supergravity
Recently, it has been shown that maximal supergravity allows for
non-supersymmetric AdS critical points that are perturbatively stable. We
investigate this phenomenon of stability without supersymmetry from the
sGoldstino point of view. In particular, we calculate the projection of the
mass matrix onto the sGoldstino directions, and derive the necessary conditions
for stability. Indeed we find a narrow window allowing for stable SUSY breaking
points. As a by-product of our analysis, we find that it seems impossible to
perturb supersymmetric critical points into non-supersymmetric ones: there is a
minimal amount of SUSY breaking in maximal supergravity.Comment: 27 pages, 1 figure. v2: two typos corrected, published versio
Metastable supergravity vacua with F and D supersymmetry breaking
We study the conditions under which a generic supergravity model involving
chiral and vector multiplets can admit viable metastable vacua with
spontaneously broken supersymmetry and realistic cosmological constant. To do
so, we impose that on the vacuum the scalar potential and all its first
derivatives vanish, and derive a necessary condition for the matrix of its
second derivatives to be positive definite. We study then the constraints set
by the combination of the flatness condition needed for the tuning of the
cosmological constant and the stability condition that is necessary to avoid
unstable modes. We find that the existence of such a viable vacuum implies a
condition involving the curvature tensor for the scalar geometry and the charge
and mass matrices for the vector fields. Moreover, for given curvature, charges
and masses satisfying this constraint, the vector of F and D auxiliary fields
defining the Goldstino direction is constrained to lie within a certain domain.
The effect of vector multiplets relative to chiral multiplets is maximal when
the masses of the vector fields are comparable to the gravitino mass. When the
masses are instead much larger or much smaller than the gravitino mass, the
effect becomes small and translates into a correction to the effective
curvature. We finally apply our results to some simple classes of examples, to
illustrate their relevance.Comment: 40 pages; v2 some clarifications added in the introduction; v3 some
typos correcte
Moduli stabilization with Fayet-Iliopoulos uplift
In the recent years, phenomenological models of moduli stabilization were
proposed, where the dynamics of the stabilization is essentially
supersymmetric, whereas an O'Rafearthaigh supersymmetry breaking sector is
responsible for the "uplift" of the cosmological constant to zero. We
investigate the case where the uplift is provided by a Fayet-Iliopoulos sector.
We find that in this case the modulus contribution to supersymmetry breaking is
larger than in the previous models. A first consequence of this class of
constructions is for gauginos, which are heavier compared to previous models.
In some of our explicit examples, due to a non-standard gauge-mediation type
negative contribution to scalars masses, the whole superpartner spectrum can be
efficiently compressed at low-energy. This provides an original phenomenology
testable at the LHC, in particular sleptons are generically heavier than the
squarks.Comment: 29 pages, 2 figure
Moduli stabilization with positive vacuum energy
We study the effect of anomalous U(1) gauge groups in string theory
compactification with fluxes. We find that, in a gauge invariant formulation,
consistent AdS vacua appear breaking spontaneously supergravity. Non vanishing
D-terms from the anomalous symmetry act as an uplifting potential and could
allow for de Sitter vacua. However, we show that in this case the gravitino is
generically (but not always) much heavier than the electroweak scale. We show
that alternative uplifting scheme based on corrections to the Kahler potential
can be compatible with a gravitino mass in the TeV range.Comment: 20 pages, 1 figur
Metastable de Sitter vacua in N=2 to N=1 truncated supergravity
We study the possibility of achieving metastable de Sitter vacua in general
N=2 to N=1 truncated supergravities without vector multiplets, and compare with
the situations arising in N=2 theories with only hypermultiplets and N=1
theories with only chiral multiplets. In N=2 theories based on a quaternionic
manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable,
as a result of the peculiar properties of the geometry. In N=1 theories based
on a Kahler manifold and a superpotential, de Sitter vacua can instead be
metastable provided the geometry satisfies some constraint and the
superpotential can be freely adjusted. In N=2 to N=1 truncations, the crucial
requirement is then that the tachyon of the mother theory be projected out from
the daughter theory, so that the original unstable vacuum is projected to a
metastable vacuum. We study the circumstances under which this may happen and
derive general constraints for metastability on the geometry and the gauging.
We then study in full detail the simplest case of quaternionic manifolds of
dimension four with at least one isometry, for which there exists a general
parametrization, and study two types of truncations defining Kahler
submanifolds of dimension two. As an application, we finally discuss the case
of the universal hypermultiplet of N=2 superstrings and its truncations to the
dilaton chiral multiplet of N=1 superstrings. We argue that de Sitter vacua in
such theories are necessarily unstable in weakly coupled situations, while they
can in principle be metastable in strongly coupled regimes.Comment: 40 pages, no figure
An Effective Description of the Landscape - II
We continue our analysis of establishing the reliability of "simple"
effective theories where massive fields are "frozen" rather than integrated
out, in a wide class of four dimensional theories with global or local N=1
supersymmetry. We extend our previous work by adding gauge fields and O(1)
Yukawa-like terms for the charged fields in the superpotential. For generic
Kaehler potentials, a meaningful freezing is allowed for chiral multiplets
only, whereas in general heavy vector fields have to properly be integrated
out. Heavy chiral fields can be frozen if they approximately sit to
supersymmetric solutions along their directions and, in supergravity, if the
superpotential at the minimum is small, so that a mass hierarchy between heavy
and light fields is ensured. When the above conditions are met, we show that
the simple effective theory is generally a reliable truncation of the full one.Comment: 20 page
Inflation with racetrack superpotential and matter field
Several models of inflation with the racetrack superpotential for the volume
modulus coupled to a matter field are investigated. In particular, it is shown
that two classes of racetrack inflation models, saddle point and inflection
point ones, can be constructed in a fully supersymmetric framework with the
matter field F-term as a source of supersymmetry breaking and uplifting. Two
models of F-term supersymmetry breaking are considered: the Polonyi model and
the quantum corrected O'Raifeartaigh model. In the former case, both classes of
racetrack inflation models differ significantly from the corresponding models
with non-supersymmetric uplifting. The main difference is a quite strong
dominance of the inflaton by the matter field. In addition, fine-tuning of the
parameters is relaxed as compared to the original racetrack models. In the case
of the racetrack inflation models coupled to the O'Raifeartaigh model, the
matter field is approximately decoupled from the inflationary dynamics. In all
of the above models the gravitino mass is larger than the Hubble scale during
inflation. The possibility of having the gravitino much lighter than the Hubble
scale is also investigated. It is very hard to construct models with light
gravitino in which the volume modulus dominates inflation. On the other hand,
models in which the inflationary dynamics is dominated by the matter field are
relatively simple and seem to be more natural.Comment: 40 pages, 13 figures, references added, typos corrected, version to
be publishe
Exact 2-point function in Hermitian matrix model
J. Harer and D. Zagier have found a strikingly simple generating function for
exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model.
In this paper we generalize their result to 2-point correlators, using Toda
integrability of the model. Remarkably, this exact 2-point correlation function
turns out to be an elementary function - arctangent. Relation to the standard
2-point resolvents is pointed out. Some attempts of generalization to 3-point
and higher functions are described.Comment: 31 pages, 1 figur
A note on instanton counting for N=2 gauge theories with classical gauge groups
We study the prepotential of N=2 gauge theories using the instanton counting
techniques introduced by Nekrasov. For the SO theories without matter we find a
closed expression for the full prepotential and its string theory gravitational
corrections. For the more subtle case of Sp theories without matter we discuss
general features and compute the prepotential up to instanton number three. We
also briefly discuss SU theories with matter in the symmetric and antisymmetric
representations. We check all our results against the predictions of the
corresponding Seiberg-Witten geometries.Comment: 24 pages, LaTeX. v2: refs added. v3: typos correcte
F-term uplifting via consistent D-terms
The issue of fine-tuning necessary to achieve satisfactory degree of
hierarchy between moduli masses, the gravitino mass and the scale of the
cosmological constant has been revisited in the context of supergravities with
consistent D-terms. We have studied (extended) racetrack models where
supersymmetry breaking and moduli stabilisation cannot be separated from each
other. We show that even in such cases the realistic hierarchy can be achieved
on the expense of a single fine-tuning. The presence of two condensates changes
the role of the constant term in the superpotential, W_0, and solutions with
small vacuum energy and large gravitino mass can be found even for very small
values of W_0. Models where D-terms are allowed to vanish at finite vevs of
moduli fields - denoted `cancellable' D-terms - and the ones where D-terms may
vanish only at infinite vevs of some moduli - denoted `non-cancellable' -
differ markedly in their properties. It turns out that the tuning with respect
to the Planck scale required in the case of cancellable D-terms is much weaker
than in the case of non-cancellable ones. We have shown that, against
intuition, a vanishing D-term can trigger F-term uplifting of the vacuum energy
due to the stringent constraint it imposes on vacuum expectation values of
charged fields. Finally we note that our models only rely on two dimensionful
parameters: M_P and W_0.Comment: 10 pages, 2 figures, plain Latex, references adde
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