N=31, D=11

We show that eleven-dimensional supergravity backgrounds with thirty one supersymmetries, N=31, admit an additional Killing spinor and so they are locally isometric to maximally supersymmetric ones. This rules out the existence of simply connected eleven-dimensional supergravity preons. We also show that N=15 solutions of type I supergravities are locally isometric to Minkowski spacetime.Comment: 17 page

The holonomy of the supercovariant connection and Killing spinors

We show that the holonomy of the supercovariant connection for M-theory backgrounds with $N$ Killing spinors reduces to a subgroup of SL(32-N,\bR)\st (\oplus^N \bR^{32-N}). We use this to give the necessary and sufficient conditions for a background to admit $N$ Killing spinors. We show that there is no topological obstruction for the existence of up to 22 Killing spinors in eleven-dimensional spacetime. We investigate the symmetry superalgebras of supersymmetric backgrounds and find that their structure constants are determined by an antisymmetric matrix. The Lie subalgebra of bosonic generators is related to a real form of a symplectic group. We show that there is a one-one correspondence between certain bases of the Cartan subalgebra of sl(32, \bR) and supersymmetric planar probe M-brane configurations. A supersymmetric probe configuration can involve up to 31 linearly independent planar branes and preserves one supersymmetry. The space of supersymmetric planar probe M-brane configurations is preserved by an SO(32,\bR) subgroup of SL(32, \bR).Comment: 27 pages, a key reference was added. v3: minor change

The Geometry of D=11 Null Killing Spinors

We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used to construct a null Killing vector. This class covers all supersymmetric time-dependent configurations and completes the classification of the most general supersymmetric configurations initiated in hep-th/0212008.Comment: 30 pages, typos corrected, reference added, new solution included in section 5.1; uses JHEP3.cl

Uniqueness of Five-Dimensional Supersymmetric Black Holes

A classification of supersymmetric solutions of five dimensional ungauged supergravity coupled to arbitrary many abelian vector multiplets is used to prove a uniqueness theorem for asymptotically flat supersymmetric black holes with regular horizons. It is shown that the near-horizon geometries of solutions for which the scalars and gauge field strengths are sufficiently regular on the horizon are flat space, AdS_3 x S^2, or the near-horizon BMPV solution. Furthermore, the only black hole which has the near-horizon BMPV geometry for its near-horizon geometry is the solution found by Chamseddine and Sabra.Comment: 15 pages, uses JHEP3.cls. Revised to match published version; reference added, minor alterations to section

Test de Zohlen y su relación con el ángulo Q en población sin dolor patelofemoral

ResumenObjetivoDeterminar qué porcentaje de una población sin dolor anterior de rodilla tiene un test de Zohlen positivo, además determinar el ángulo Q de esta población y buscar si existe alguna relación entre la positividad del test de Zohlen y alteraciones en el ángulo Q.Material y métodoEstudio descriptivo-prospectivo observacional. Aplicación del test de Zohlen y medición del ángulo Q. La población se dividió en 2 grupos: test de Zohlen positivo y test de Zohlen negativo. Cuantificación y comparación de medias del ángulo Q en los dos grupos.Resultados90 sujetos evaluados, promedio de edad 20,18 años (18-40). Veinte sujetos (22,2%) con test de Zohlen positivo. Ángulo Q promedio en los sujetos con test de Zohlen negativo: 14,95°; ángulo Q promedio en los sujetos con test de Zohlen positivo: 16,9° (p < 0,05).Ángulo Q promedio en hombres con test de Zohlen negativo13,4°; ángulo Q promedio en hombres con test de Zohlen positivo: 16° (p < 0,05). Ángulo Q promedio en mujeres con test de Zohlen negativo: 16,5°; ángulo Q promedio en mujeres con test de Zohlen positivo: 18°, sin diferencias estadísticamente significativas entre ambos grupos.ConclusionesEl test de Zohlen tiene una correlación positiva con el ángulo Q en sujetos de sexo masculino. Dada la correlación entre un ángulo Q alterado y la presencia de dolor anterior de rodilla, en los pacientes que presentan un test de Zohlen positivo sin haber consultado por dolor anterior de rodilla, la prevención primaria de dolor anterior de rodilla puede ser de utilidad.AbstractObjectiveTo determine the percentage of a population without anterior knee pain with a positive Zohlen test, and also to determine the Q angle of this population and to determine if there is any relationship between the Zohlen test and Q angle anomalies.MethodsA prospective observational study was conducted in which Zohleńs test was applied and the Q angle was measured. The population was divided into 2 groups: Zohleńs positive and Zohleńs negative. Q angle was compared in the 2 groups.ResultsThe study included 90 subjects, with a mean age 20.18 years (18-40), of whom 20 subjects (22.2%) had positive Zohleńs test. The mean Q angle in subjects with negative Zohleńs test was 14.95°, and the mean Q angle in subjects with positive Zohleńs test was 16,9° (p<.05). The mean Q angle in men with negative Zohleńs test was 13.4°, and the mean Q angle in men with positive Zohleńs test was 16° (p < .05). The mean Q angle in women with negative Zohleńs test was 16.5°, with a mean Q angle of 18° in women with positive Zohleńs test, with no statistically significant differences found between groups.ConclusionsZohleńs test has a positive correlation with the Q angle in male subjects. Given the correlation between the Q angle and the presence of anterior knee pain in patients who have a positive test without symptoms, primary prevention of anterior knee pain can be achieved

The Geometry of D=11 Killing Spinors

We propose a way to classify all supersymmetric configurations of D=11 supergravity using the G-structures defined by the Killing spinors. We show that the most general bosonic geometries admitting a Killing spinor have at least a local SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the former case we determine what kind of local SU(5) structure is present and show that almost all of the form of the geometry is determined by the structure. We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D=11 Godel solution.Comment: 36 pages. Typos corrected and discussion on G-structures improved. Final version to appear in JHE

Marginal Deformations of Field Theories with AdS_4 Duals

We generate new AdS_4 solutions of D=11 supergravity starting from AdS_4 x X_7 solutions where X_7 has U(1)^3 isometry. We consider examples where X_7 is weak G_2, Sasaki-Einstein or tri-Sasakian, corresponding to d=3 SCFTs with N=1,2 or 3 supersymmetry, respectively, and where the deformed solutions preserve N=1,2 or 1 supersymmetry, respectively. For the special cases when X_7 is M(3,2), Q(1,1,1) or N(1,1)_I we identify the exactly marginal deformation in the dual field theory. We also show that the volume of supersymmetric 5-cycles of N(1,1)_I agrees with the conformal dimension predicted by the baryons of the dual field theory.Comment: 28 pages, 2 figures; v2. typos correcte

Fast k-NN classifier for documents based on a graph structure

In this paper, a fast k nearest neighbors (k-NN) classifier for documents is presented. Documents are usually represented in a high-dimensional feature space, where terms appeared on it are treated as features and the weight of each term reflects its importance in the document. There are many approaches to find the vicinity of an object, but their performance drastically decreases as the number of dimensions grows. This problem prevents its application for documents. The proposed method is based on a graph index structure with a fast search algorithm. It’s high selectivity permits to obtain a similar classification quality than exhaustive classifier, with a few number of computed distances. Our experimental results show that it is feasible the use of the proposed method in problems of very high dimensionality, such as Text Mining

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 $Spin(10,1)$ 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

A Brane Teaser

In this note we study the puzzle posed by two M5-branes intersecting on a string (or equivalently, a single M5-brane wrapping a holomorphic four-cycle in C^4). It has been known for a while that this system is different from all other configurations built using self-intersecting M-branes; in particular the corresponding supergravity solution exhibits various curious features which have remained unexplained. We propose that the resolution to these puzzles lies in the existence of a non-zero two-form on the M5-brane world-volume.Comment: 21 pages. References adde