Half-BPS M2-brane orbifolds

Smooth Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical space form, whence isometric to the quotient of the round 7-sphere by a freely-acting finite subgroup of SO(8). The classification is given in terms of ADE subgroups of the quaternions embedded in SO(8) as the graph of an automorphism. In this paper we extend this classification by dropping the requirement that the background be smooth, so that X is now allowed to be an orbifold of the round 7-sphere. We find that if the background preserves more than half of the supersymmetry, then it is automatically smooth in accordance with the homogeneity conjecture, but that there are many half-BPS orbifolds, most of them new. The classification is now given in terms of pairs of ADE subgroups of quaternions fibred over the same finite group. We classify such subgroups and then describe the resulting orbifolds in terms of iterated quotients. In most cases the resulting orbifold can be described as a sequence of cyclic quotients.Comment: 51 pages; v3: substantial revision (20% longer): we had missed some cases, but the paper now includes a check of our results via comparison with extant classification of finite subgroups of SO(4

Half-BPS quotients in M-theory: ADE with a twist

We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 which are at least half BPS; equivalently, smooth quotients of the round 7-sphere by finite subgroups of SO(8) which admit an (N>3)-dimensional subspace of Killing spinors. The classification is given in terms of pairs consisting of an ADE subgroup of SU(2) and an automorphism defining its embedding in SO(8). In particular we find novel half-BPS quotients associated with the subgroups of type D_n (for n>5), E_7 and E_8 and their outer automorphisms.Comment: 16 pages; V2: notational inconsistencies addressed, final version to be published in JHE

Metric Lie 3-algebras in Bagger-Lambert theory

We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We classify metric Lie 3-algebras of signature (2,p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product. We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2,p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.Comment: 38 page

On the Lie-algebraic origin of metric 3-algebras

Since the pioneering work of Bagger-Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal Chern-Simons theories whose main ingredient is a metric 3-algebra. On the other hand, many of these theories have been shown to allow for a reformulation in terms of standard gauge theory coupled to matter, where the 3-algebra does not appear explicitly. In this paper we reconcile these two sets of results by pointing out the Lie-algebraic origin of some metric 3-algebras, including those which have already appeared in three-dimensional superconformal Chern-Simons theories. More precisely, we show that the real 3-algebras of Cherkis-Saemann, which include the metric Lie 3-algebras as a special case, and the hermitian 3-algebras of Bagger-Lambert can be constructed from pairs consisting of a metric real Lie algebra and a faithful (real or complex, respectively) unitary representation. This construction generalises and we will see how to construct many kinds of metric 3-algebras from pairs consisting of a real metric Lie algebra and a faithful (real, complex or quaternionic) unitary representation. In the real case, these 3-algebras are precisely the Cherkis-Saemann algebras, which are then completely characterised in terms of this data. In the complex and quaternionic cases, they constitute generalisations of the Bagger-Lambert hermitian 3-algebras and anti-Lie triple systems, respectively, which underlie N=6 and N=5 superconformal Chern-Simons theories, respectively. In the process we rederive the relation between certain types of complex 3-algebras and metric Lie superalgebras.Comment: 29 pages (v4: really final version to appear in CMP. Example 7 has been improved.

Gauging of Nonlinearly Realized Symmetries

A representation of a subgroup H of a finite-dimensional group G can be used to induce a nonlinear realization of G. If the nonlinearly realized symmetry is gauged, then the BRST charge can be related by a similarity transformation to the BRST charge for the gauged linear realization of H (plus a cohomologically trivial piece). It is shown that the relation between the two BRST charges is a reflection of the fact that they can be interpreted geometrically as expressions for the exterior derivative on G relative to two different bases, and an explicit expression for the generator of the similarity transformation is obtained. This result is applied in an infinite-dimensional setting, where it yields the similarity transformation used by Ishikawa and Kato to prove the equivalence of the Berkovits-Vafa superstring with the underlying bosonic string theory.Comment: 14 pages, LATEX documen

Tratado espiritual, en el qual se contienen dos obras, la primera trata de la venta de Judas quando vendió a nuestro Redemptor Jesu Christo y de como ay muchos Judas que cada día le venden ; y la otra obra, el negamiento y llanto de Sant Pedro, sobre aquella glosa que dize, Quien es Dios y quien soy yo

Copia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 2009-201

Towards an evaluation model of emotional competencies in nurse students

En los últimos años múltiples estudios han demostrado la importancia de la inteligencia emocional para el desarrollo profesional óptimo de los alumnos de enfermería. Este trabajo nace como respuesta ante la necesidad de una herramienta que permita medir de forma clara y objetiva las competencias emocionales de los estudiantes de enfermería. Tras haber realizado una revisión bibliográfica de artículos científicos y bibliotecas online entre las que destacan Pubmed, Medline Plus, ENFISPO y SCIELO en la que se ha tenido en cuenta la fecha de publicación y aquellos con mayor número de citaciones. Se ha analizado los diferentes métodos para evaluar este factor, tales como las medidas de autoinforme, las medidas de habilidad o el método ECOE, concluimos que la información que aportan, aunque pertinente podría estar más adaptada al contexto académico. En el presente trabajo, se propone una nueva herramienta que pretende reunir las ventajas de los tres anteriores y completar la información que aportan a través de un rol-playing en el que se evaluará al alumno mediante una rúbrica sencilla, de forma que cualquiera pueda emplearla sin formación específica. De este modo, el alumno identificará las áreas de mejora en su desempeño y los aspectos correctos de su práctica, de manera que esta rúbrica, no solamente sirva como un instrumento de evaluación sino que además pueda ser útil para el desarrollo de las competencias profesionales del alumno de enfermeríaDuring the past years, multiple studies have demonstrated the importance of emotional intelligence for the positive professional development of nurse students. This document has been created due to the need of an instrument that can allow us to measure clearly and objectively the emotional competencies of the nurse students. After having done a bibliographical review of scientific articles and libraries online such as Pubmed, Medline Plus, ENFISPO and SCIELO in which we have taken into account the publication date and the number of citations, we have analysed the different existing methods to evaluate this factor, such as self-report- measures, the ability measures or the ECOE method, we conclude that the information they provide, even though it is pertinent, could be better adapted to the academic environment. In this project, we suggest a new tool that will include the advantages of the three mentioned above and complete the information with the role-playing that will evaluate the student according to a simple rubric, this way anyone can use it without previous specialized knowledge. Consequently, the student will be able to identify improvements in their performance and recognize the correct aspects of their enactment, as a result of this, apart from using it as a tool to evaluate; it can be considered for the personal development of the nurse student.Fac. de Enfermería, Fisioterapia y PodologíaTRUEsubmitte