We revisit from a modern bootstrap perspective the longstanding problem of solving QCD in the large N limit. We derive universal bounds on the effective field theory of massless pions by imposing the full set of positivity constraints that follow from 2 → 2 scattering. Some features of our exclusion plots have intriguing connections with hadronic phenomenology. The exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that large N QCD may sit at this kink. We critically examine this possibility, developing in the process a partial analytic understanding of the geometry of the bounds.

We study the self-gravitating Abrikosov vortex in curved space with and with-out a (negative) cosmological constant, considering both singular and non-singular solutions with an eye to hairy black holes. In the asymptotically flat case, we find that non-singular vortices round off the singularity of the point particle’s metric in 3 dimensions, whereas singular solutions consist of vortices holding a conical singularity at their core. There are no black hole vortex solutions. In the asymptotically AdS case, in addition to these solutions there exist singular solutions containing a BTZ black hole, but they are always hairless. So we find that in contrast with 4-dimensional ’t Hooft-Polyakov monopoles, which can be regarded as their higher-dimensional analogues, Abrikosov vortices cannot hold a black hole at their core. We also describe the implications of these results in the context of AdS/CFT and propose an interpretation for their CFT dual along the lines of the holographic superconductor.

Este artículo analiza la relación entre el desarrollo de la competencia social y ciudadana y la utilización de metodologías didácticas activas en las aulas de secundaria. El contexto se sitúa en el ámbito educativo de Cataluña a partir del análisis de cuatro unidades didácticas que plantean objetivos competenciales con métodos que facilitan la indagación y el análisis social conocidos como aprendizaje por descubrimiento.  Para el tratamiento de los datos recogidos se ha utilizado una metodología cualitativa a partir de una observación directa no participante en las aulas y de un análisis lexicométrico, a partir del software Iramuteq, desde tres dimensiones: el desarrollo de las unidades didácticas, la metodología docente y el desarrollo de la competencia social y ciudadana. Los resultados se presentan a partir de los conceptos y habilidades que caracterizan la labor del docente y de los estudiantes, y también con el análisis de los gráficos originados con el software y con el uso de reflexiones narrativas recogidas durante la observación. Las conclusiones constatan el protagonismo del estudiante en la construcción de su aprendizaje, así como el papel determinante del profesor como guía en la construcción de la competencia social y ciudadana. This article analyzes the relationship between the development of social and civic competence and the use of active didactic methodologies in secondary school classrooms. The context is located in the educational field of Catalonia through the analysis of four didactic units that sets competency aims with methods that facilitate inquiry and social analysis known as discovery learning. For the treatment of the collected data, a qualitative methodology has been used from a direct non-participant observation in the classrooms and from a lexicometry analysis from three aspects: the development of the teaching units, the methodology used by the docent and the development of social competence and citizen. The analysis of the texts has been done with the Iramuteq software. The results are presented from the concepts and skills that characterize the work of the teacher and the students with the analysis of the graphics originated with the software and with the use of narrative reflections collected during the observation. The conclusions confirm the protagonism of the student in the construction of their learning as well as the determining role of the teacher as a guide in the construction of social and civic competence