79 research outputs found
SU(3)-instantons and -heterotic string solitons
Necessary and sufficient conditions to the existence of a hermitian
connection with totally skew-symmetric torsion and holonomy contained in SU(3)
are given. Non-compact solution to the supergravity-type I equations of motion
with non-zero flux and non-constant dilaton is found in dimensions 6.
Non-conformally flat non-compact solutions to the supergravity-type I equations
of motion with non-zero flux and non-constant dilaton are found in dimensions 7
and 8. A Riemannian metric with holonomy contained in arises from our
considerations and Hitchin's flow equations, which seems to be new. Compact
examples of and instanton satisfying the anomaly
cancellation conditions are presented.Comment: LaTex, 22 pages, Corrected anomaly cancellation, final version to
appear in Commun. Math. Phy
Kappa symmetry, generalized calibrations and spinorial geometry
We extend the spinorial geometry techniques developed for the solution of
supergravity Killing spinor equations to the kappa symmetry condition for
supersymmetric brane probe configurations in any supergravity background. In
particular, we construct the linear systems associated with the kappa symmetry
projector of M- and type II branes acting on any Killing spinor. As an example,
we show that static supersymmetric M2-brane configurations which admit a
Killing spinor representing the SU(5) orbit of are generalized
almost hermitian calibrations and the embedding map is pseudo-holomorphic. We
also present a bound for the Euclidean action of M- and type II branes embedded
in a supersymmetric background with non-vanishing fluxes. This leads to an
extension of the definition of generalized calibrations which allows for the
presence of non-trivial Born-Infeld type of fields in the brane actions.Comment: 9 pages, latex, references added and minor change
Imaging Biomarkers in Alzheimer's Disease: A Practical Guide for Clinicians.
Although recent developments in imaging biomarkers have revolutionized the diagnosis of Alzheimer's disease at early stages, the utility of most of these techniques in clinical setting remains unclear. The aim of this review is to provide a clear stepwise algorithm on using multitier imaging biomarkers for the diagnosis of Alzheimer's disease to be used by clinicians and radiologists for day-to-day practice. We summarized the role of most common imaging techniques and their appropriate clinical use based on current consensus guidelines and recommendations with brief sections on acquisition and analysis techniques for each imaging modality. Structural imaging, preferably MRI or alternatively high resolution CT, is the essential first tier of imaging. It improves the accuracy of clinical diagnosis and excludes other potential pathologies. When the results of clinical examination and structural imaging, assessed by dementia expert, are still inconclusive, functional imaging can be used as a more advanced option. PET with ligands such as amyloid tracers and 18F-fluorodeoxyglucose can improve the sensitivity and specificity of diagnosis particularly at the early stages of the disease. There are, however, limitations in using these techniques in wider community due to a combination of lack of facilities and expertise to interpret the findings. The role of some of the more recent imaging techniques including tau imaging, functional MRI, or diffusion tensor imaging in clinical practice, remains to be established in the ongoing and future studies.No other source of fundin
Vanishing Preons in the Fifth Dimension
We examine supersymmetric solutions of N=2, D=5 gauged supergravity coupled
to an arbitrary number of abelian vector multiplets using the spinorial
geometry method. By making use of methods developed in hep-th/0606049 to
analyse preons in type IIB supergravity, we show that there are no solutions
preserving exactly 3/4 of the supersymmetry.Comment: 19 pages, latex. Reference added, and further modification to the
introductio
The spinorial geometry of supersymmetric heterotic string backgrounds
We determine the geometry of supersymmetric heterotic string backgrounds for
which all parallel spinors with respect to the connection with
torsion , the NSNS three-form field strength, are Killing. We find
that there are two classes of such backgrounds, the null and the timelike. The
Killing spinors of the null backgrounds have stability subgroups
K\ltimes\bR^8 in , for , SU(4), , and , and the Killing spinors of the timelike backgrounds have
stability subgroups , SU(3), SU(2) and . The former admit a single
null -parallel vector field while the latter admit a timelike and
two, three, five and nine spacelike -parallel vector fields,
respectively. The spacetime of the null backgrounds is a Lorentzian
two-parameter family of Riemannian manifolds with skew-symmetric torsion.
If the rotation of the null vector field vanishes, the holonomy of the
connection with torsion of is contained in . The spacetime of time-like
backgrounds is a principal bundle with fibre a Lorentzian Lie group and
base space a suitable Riemannian manifold with skew-symmetric torsion. The
principal bundle is equipped with a connection which determines the
non-horizontal part of the spacetime metric and of . The curvature of
takes values in an appropriate Lie algebra constructed from that of
. In addition has only horizontal components and contains the
Pontrjagin class of . We have computed in all cases the Killing spinor
bilinears, expressed the fluxes in terms of the geometry and determine the
field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change
SU(3)-structures on submanifolds of a Spin(7)-manifold
Local SU(3)-structures on an oriented submanifold of Spin(7)-manifold are
determined and their types are characterized in terms of the shape operator and
the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084}
and Calabi \cite{MR24 #A558} examples is given. It is shown that the product of
a Cayley plane and a minimal surface lying in a four-dimensional orthogonal
Cayley plane with the induced complex structure from the octonions described by
Bryant in \cite{MR89b:53084} admits a holomorphic local complex volume form
exactly when it lies in a three-plane, i.e. it coincides with the example
constructed by Calabi in \cite{MR24 #A558}. In this case the holomorphic
(3,0)-form is parallel with respect to the unique Hermitian connection with
totally skew-symmetric torsion.Comment: 25 pages, no figures, some improvements and clarifications are made,
final version to appear in Diff. Geom. App
Maximally Minimal Preons in Four Dimensions
Killing spinors of N=2, D=4 supergravity are examined using the spinorial
geometry method, in which spinors are written as differential forms. By making
use of methods developed in hep-th/0606049 to analyze preons in type IIB
supergravity, we show that there are no simply connected solutions preserving
exactly 3/4 of the supersymmetry.Comment: 18 pages. References added, comments added discussing the possibility
of discrete quotients of AdS(4) preserving 3/4 supersymmetry
Systematics of M-theory spinorial geometry
We reduce the classification of all supersymmetric backgrounds in eleven
dimensions to the evaluation of the supercovariant derivative and of an
integrability condition, which contains the field equations, on six types of
spinors. We determine the expression of the supercovariant derivative on all
six types of spinors and give in each case the field equations that do not
arise as the integrability conditions of Killing spinor equations. The Killing
spinor equations of a background become a linear system for the fluxes,
geometry and spacetime derivatives of the functions that determine the spinors.
The solution of the linear system expresses the fluxes in terms of the geometry
and specifies the restrictions on the geometry of spacetime for all
supersymmetric backgrounds. We also show that the minimum number of field
equations that is needed for a supersymmetric configuration to be a solution of
eleven-dimensional supergravity can be found by solving a linear system. The
linear systems of the Killing spinor equations and their integrability
conditions are given in both a timelike and a null spinor basis. We illustrate
the construction with examples.Comment: 46 pages. v2: systematics of a null spinor basis is included in
section
New half supersymmetric solutions of the heterotic string
We describe all supersymmetric solutions of the heterotic string which
preserve 8 supersymmetries and show that are distinguished by the holonomy,
, of the connection, , with skew-symmetric
torsion. The solutions are principal
bundles over a 4-dimensional hyper-K\"ahler manifold equipped with a
anti-self-dual connection and fibre group which has Lie algebra,
{\mathfrak Lie} (G)=\bR^{5,1}, \mathfrak{sl}(2,\bR)\oplus \mathfrak{su}(2)
or . Some of the solutions have the interpretation as 5-branes
wrapped on with transverse space any hyper-K\"ahler 4-dimensional manifold.
We construct new solutions for {\mathfrak Lie} (G)=\mathfrak{sl}(2,\bR)\oplus
\mathfrak{su}(2) and show that are characterized by 3 integers and have
continuous moduli. There is also a smooth family in this class with one
asymptotic region and the dilaton is bounded everywhere on the spacetime. We
also demonstrate that the worldvolume theory of the backgrounds with holonomy
SU(2) can be understood in terms of gauged WZW models for which the gauge
fields are composite. The {\rm hol}(\hat\nabla) \subseteq\bR^8 solutions are
superpositions of fundamental strings and pp-waves in flat space, which may
also include a null rotation. The heterotic
string backgrounds which preserve 8 supersymmetries are Lorentzian group
manifolds.Comment: 31 pages, minor corrections, analysis improved and more references
adde
The spinorial geometry of supersymmetric backgrounds
We propose a new method to solve the Killing spinor equations of
eleven-dimensional supergravity based on a description of spinors in terms of
forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We
give the canonical form of Killing spinors for N=2 backgrounds provided that
one of the spinors represents the orbit of Spin(1,10) with stability subgroup
SU(5). We directly solve the Killing spinor equations of N=1 and some N=2, N=3
and N=4 backgrounds. In the N=2 case, we investigate backgrounds with SU(5) and
SU(4) invariant Killing spinors and compute the associated spacetime forms. We
find that N=2 backgrounds with SU(5) invariant Killing spinors admit a timelike
Killing vector and that the space transverse to the orbits of this vector field
is a Hermitian manifold with an SU(5)-structure. Furthermore, N=2 backgrounds
with SU(4) invariant Killing spinors admit two Killing vectors, one timelike
and one spacelike. The space transverse to the orbits of the former is an
almost Hermitian manifold with an SU(4)-structure and the latter leaves the
almost complex structure invariant. We explore the canonical form of Killing
spinors for backgrounds with extended, N>2, supersymmetry. We investigate a
class of N=3 and N=4 backgrounds with SU(4) invariant spinors. We find that in
both cases the space transverse to a timelike vector field is a Hermitian
manifold equipped with an SU(4)-structure and admits two holomorphic Killing
vector fields. We also present an application to M-theory Calabi-Yau
compactifications with fluxes to one-dimension.Comment: Latex, 54 pages, v2: clarifications made and references added. v3:
minor changes. v4: minor change
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