N=2 minimal conformal field theories and matrix bifactorisations of x^d

We establish an action of the representations of N=2-superconformal symmetry on the category of matrix factorisations of the potentials x^d and x^d-y^d for d odd. More precisely we prove a tensor equivalence between (a) the category of Neveu–Schwarz-type representa-tions of the N = 2 minimal super vertex operator algebra at central charge 3–6/d, and (b) a full subcategory of graded matrix factorisations of the potential x^d − y^d . The subcategory in (b) is given by permutation-type matrix factorisations with consecutive index sets. The physical motivation for this result is the Landau–Ginzburg/conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [BR], where an isomorphism of fusion rules was established

OB stars at the lowest Local Group metallicity: GTC-OSIRIS observations of Sextans A

Our aim is to find and classify OB stars in Sextans A, to later determine accurate stellar parameters of these blue massive stars in this low metallicity region $(Z \sim 0.1 \rm Z_{\odot})$. Using UBV photometry, the reddening-free index Q and GALEX imaging, we built a list of blue massive star candidates in Sextans A. We obtained low resolution (R $\sim$ 1000) GTC-OSIRIS spectra for a fraction of them and carried out spectral classification. For the confirmed O-stars we derive preliminary stellar parameters. The target selection criteria and observations were successful and have produced the first spectroscopic atlas of OB-type stars in Sextans A. From the whole sample of 18 observed stars, 12 were classified as early OB-types, including 5 O-stars. The radial velocities of all target stars are in agreement with their Sextans A membership, although three of them show significant deviations. We determined the stellar parameters of the O-type stars using the stellar atmosphere code FASTWIND, and revisited the sub-SMC temperature scale. Two of the O-stars are consistent with relatively strong winds and enhanced helium abundances, although results are not conclusive. We discuss the position of the OB stars in the HRD. Initial stellar masses run from slightly below 20 up to 40 solar masses. The target selection method worked well for Sextans A, confirming the procedure developed in Garcia \& Herrero (2013). The stellar temperatures are consistent with findings in other galaxies. Some of the targets deserve follow-up spectroscopy because of indications of a runaway nature, an enhanced helium abundance or a relatively strong wind. We observe a correlation between HI and OB associations similar to the irregular galaxy IC1613, confirming the previous result that the most recent star formation of Sextans A is currently on-going near the rim of the H\,{\sc I} cavity

Una pieza más de un género puzzle: una nueva especie de Iberobathynella Schminke, 1973 (Syncarida, Bathynellacea, Parabathynellidae) en la Península Ibérica

A new Iberian species of the genus Iberobathynella is described from the groundwater of Ojo Guareña cave, in the north of Spain (Burgos). The new species belongs to the subgenus Espanobathynella and presents a unique combination of characters, as follow: female thoracopod 8 with wrinkled cuticle and 1 tooth (the rest of species in this subgenus show a smooth cuticle); seven-eight spines on the furca; 10-12 spines on the sympod, four barbed setae on the exopod and an unarmed endopod of the uropod; labrum with 9 main teeth in the female and 8 in the male; maxilla with one, four and 15 setae on its three segments, respectively; seven teeth on the distal segment of the maxillule; seven teeth on the pars incisive and seven-nine teeth on the pars molaris of the mandible and antennule with 7 segments.Se describe una nueva especie del género Iberobathynella (consta de 21 especies endémicas de la Península Ibérica) encontrada en la cueva más grande de España, Ojo Guareña (Burgos). La nueva especie pertenece al subgénero Iberobathynella (Espanobathynella) compuesto por 4 especies, contando ésta. Este subgénero sólo se había encontrado hasta la fecha en 2 áreas muy pequeñas de Asturias y Cantabria, y siempre en agua subterránea de cuevas. La nueva especie presenta una combinación de caracteres única: el pereiopodo 8 de la hembra tiene la cutícula rugosa (el resto de especies del subgénero la tiene lisa) y una sola fanera; tiene 7-8 espinas en la furca; el simpodio del urópodo consta de 10-12 espinas, tiene 4 sedas ciliadas en el exopodio y carece de sedas en el endopodio; el labro con 9 dientes principales en la hembra y 8 en el macho (número habitual en el género); la maxila tiene 1, 4 y 15 sedas, respectivamente, en sus 3 segmentos; la maxílula consta de 7 dientes en el segmento distal; la mandíbula tiene 7 dientes en la pars incisiva y entre 7 y 9 en la pars molaris, y la anténula tiene 7 segmentos

Divergencia genética en especies crípticas de agua subterránea: primeras secuencias COI obtenidas de la familia Bathynellidae (Crustacea, Syncarida, Bathynellacea)

The biodiversity of groundwater fauna remains poorly known and understood. Groundwater biodiversity studies are strongly affected by habitat inaccessibility and taxonomic crisis. The objective of this work was to investigate levels of genetic divergence across populations of Bathynellacea, a small crustacean group that lives exclusively in groundwater, in order to evaluate the extent of cryptic speciation in morphologically constrained clades. Partial sequences of cytochrome oxidase I (COI) have been obtained, for the first time in Bathynellidae. Specimens analyzed of the genus Vejdovskybathynella were obtained from six populations morphologically assignable to a single species; all of them are located in different areas of one of the largest karst systems (110 km of galleries topographied) known in Spain. The analyses of molecular data demonstrate the presence of three highly divergent genetic units, possibly corresponding to undescribed new species. The results of this study provide the first molecular data that complement morphological knowledge in order to address phylogenetic studies to try to resolve the relations between genera and species of the Bathynellidae family. We conclude that the evolutionary scenario of this special group of subterranean crustaceans cannot be revealed only by using morphological information due to the presence of very old lineages of cryptic species, as has been brought to light with the molecular data obtained here.La biodiversidad de la fauna de las aguas subterráneas sigue siendo poco conocida. Los estudios de diversidad biológica de las aguas subterráneas se ven negativamente afectados por la inaccesibilidad del hábitat y la crisis taxonómica. El objetivo de este trabajo es estudiar los niveles de divergencia genética de poblaciones de Bathynellacea, un pequeño grupo de crustáceos que viven exclusivamente en las aguas subterráneas, para evaluar la extensión de la especiación críptica en clados morfológicamente constreñidos. Las secuencias parciales de citocromo oxidasa I (COI) se han obtenido, por primera vez, de varios ejemplares de la familia Bathynellidae. Los ejemplares analizados del género Vejdovskybathynella proceden de seis poblaciones, morfológicamente asignables a una única especie, de uno de los sistemas kársticos más grandes de España (110 km de galerías topografiadas). El análisis de datos moleculares demuestra la presencia de tres unidades con elevada divergencia genética, dos de ellas posiblemente correspondientes a nuevas especies sin describir. Los resultados de este estudio proporcionan los primeros datos moleculares que permiten complementar el conocimiento morfológico para abordar estudios filogenéticos que ayuden a resolver las relaciones de parentesco de las especies de diferentes géneros de la familia Bathynellidae. Podemos concluir que el escenario evolutivo de este grupo de crustáceos subterráneos no se puede revelar sólo con información morfológica debido a la presencia de linajes muy antiguos de especies crípticas que parecen salir a la luz sólo con datos moleculares como los obtenidos en este trabajo

Ensayo sobre la evaluación de la extinción en hábitats extremos

Inference and estimation are the Achilles heel of many biological disciplines. The validation of results is the first step before taking any further decision. In Biodiversity studies the technical problems in validation are similar to those faced in other disciplines. The main difference with areas like medicine is that a validation error in the latter can easily take you to court, but very few responsibilities apart from moral or ethical ones generally derive from a faulty estimation or validation in Biodiversity. However, many political decisions concerning conservation issues, which in many cases affect powerful economic interests depend on the reliability of those biodiversity studies. Getting good, reliable information is not always easy, and this explains in part, the success of critical voices like Simon (1998) and Lomborg (2001). New methodologies like Population Viability Analysis has been developed to take advantage of the potential information contained in periodical sampling. We apply it to a peculiar and difficult to study fauna: the fauna of the aquatic subterranean environment. Lack of regular information and scarcity of the fauna due to difficulty to reach their proper habitat are the main problems that confront this analysis. However, despite its limitations, the analysis points towards a need to better understand the structure of the subterranean habitat from “an animal point of view” and the need of more regular sampling at the same time that the other environmental parameters are taken.La inferencia y la estima son el talón de Aquiles de muchas disciplinas biológicas. La validación de resultados es el primer paso antes de tomar decisiones ulteriores. En estudios de Biodiversidad los problemas técnicos de validación son semejantes a los que se enfrentan otras disciplinas. La principal diferencia con áreas como Medicina es que un error en validación en ésta última puede terminar fácilmente en el juzgado, pero muy pocas responsabilidades, aparte de la éticas o morales suelen afectar a estimas o validaciones defectuosas de Biodiversidad. Sin embargo, muchas decisiones políticas en relación a la conservación de especies y habitats, que en muchos casos implican poderosos intereses económicos, dependen precisamente de la fiabilidad de los estudios de biodiversidad. Obtener una información buena y fiable no es siempre fácil y explica, en parte, el éxito de voces críticas como Simon (1998) o Lomborg (2001). En este trabajo revisamos uno de los problemas de estimación en un habitat especialmente difícil, el medio subterráneo acuático. La carencia de información periódica y la escasez de esta fauna, debido principalmente a las dificultades de acceso a su habitat, son los principales problemas que hemos encontrado al tratar de aplicar análisis PVA (Populations Viability Analysis). No obstante, a pesar de la escasez de datos consistentes, este análisis pone de manifiesto la necesidad de entender mejor la estructura del habitat subterráneo, en lo que respecta a la distribución de su fauna y la necesidad de realizar más muestreos y de realizarlos con mayor regularidad

WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials

In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the text books on quantum mechanics, whereas the second one is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the Rayleigh--Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.Comment: Accepted in Modern Physics Letters

White dwarfs as test objects of Lorentz violations

In the present work the thermodynamical properties of bosonic and fermionic gases are analyzed under the condition that a modified dispersion relation is present. This last condition implies a breakdown of Lorentz symmetry. The implications upon the condensation temperature will be studied, as well, as upon other thermodynamical variables such as specific heat, entropy, etc. Moreover, it will be argued that those cases entailing a violation of time reversal symmetry of the motion equations could lead to problems with the concept of entropy. Concerning the fermionic case it will be shown that Fermi temperature suffers a modification due to the breakdown of Lorentz symmetry. The results will be applied to white dwarfs and the consequences upon the Chandrasekhar mass--radius relation will be shown. The possibility of resorting to white dwarfs for the testing of modified dispersion relations is also addressed. It will be shown that the comparison of the current observations against the predictions of our model allows us to discard some values of one of the parameters appearing in the modifications of the dispersion relation.Comment: Accepted in Classical and Quantum Gravitatio