On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds

We consider type IIB string in the two plane-wave backgrounds which may be interpreted as special limits of the AdS_3 x S^3 metric supported by either the NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a direct generalization of the Nappi-Witten model, with its spectrum being similar to that of strings in constant magnetic field. The R-R model can be solved in the light-cone gauge, where the Green-Schwarz action describes 4 massive and 4 massless copies of free bosons and fermions. We find the spectra of the two string models and study the asymptotic density of states. We also discuss a more general class of exactly solvable plane-wave models with reduced supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.

Supersymmetry of gravitational ground states

A class of black objects which are solutions of pure gravity with negative cosmological constant are classified through the mapping between the Killing spinors of the ground state and those of the transverse section. It is shown that these geometries must have transverse sections of constant curvature for spacetime dimensions d below seven. For d > 6, the transverse sections can also be Euclidean Einstein manifolds. In even dimensions, spacetimes with transverse section of nonconstant curvature exist only in d = 8 and 10. This classification goes beyond standard supergravity and the eleven dimensional case is analyzed. It is shown that if the transverse section has negative scalar curvature, only extended objects can have a supersymmetric ground state. In that case, some solutions are explicitly found whose ground state resembles a wormhole.Comment: 16 pages, CECS style, minor correction

Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings

We perform the characterization program for the supersymmetric configurations and solutions of the $\mathcal{N}=1$, $d=5$ Supergravity Theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugins. By using the conditions yielded by the characterization program, new exact supersymmetric solutions are found in the $SO(4,1)/SO(4)$ model for the hyperscalars and with $SU(2)\times U(1)$ as the gauge group. The solutions also content non-trivial vector and massive tensor fields, the latter being charged under the U(1) sector of the gauge group and with selfdual spatial components. These solutions are black holes with $AdS_2 \times S^3$ near horizon geometry in the gauged version of the theory and for the ungauged case we found naked singularities. We also analyze supersymmetric solutions with only the scalars $\phi^x$ of the vector/tensor multiplets and the metric as the non-trivial fields. We find that only in the null class the scalars $\phi^x$ can be non-constant and for the case of constant $\phi^x$ we refine the classification in terms of the contributions to the scalar potential.Comment: Minor changes in wording and some typos corrected. Version to appear in Class. Quantum Grav. 38 page

Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity

We find a complete characterization of all the supersymmetric solutions of non-Abelian gauged N=1,d=5 supergravity coupled to vector multiplets and hypermultiplets: the generic forms of the metrics as functions of the scalars and vector fields plus the equations that all these must satisfy. These equations are now a complicated non-linear system and there it seems impossible to produce an algorithm to construct systematically all supersymmetric solutions.Comment: Some references and two comments adde

All the supersymmetric solutions of N=1,d=5 ungauged supergravity

We classify the supersymmetric solutions of ungauged N=1 d=5 SUGRA coupled to vector multiplets and hypermultiplets. All the solutions can be seen as deformations of solutions with frozen hyperscalars. We show explicitly how the 5-dimensional Reissner-Nordstrom black hole is deformed when hyperscalars are living on SO(4,1)/SO(4) are turned on, reducing its supersymmetry from 1/2 to 1/8. We also describe in the timelike and null cases the solutions that have one extra isometry and can be reduced to N=2,d=4 solutions. Our formulae allows the uplifting of certain N=2,d=4 black holes to N=1,d=5 black holes on KK monopoles or to pp-waves propagating along black strings.Comment: Some typos fixed and some paragraphs improved. 44 pages, Latex 2e file, no figures. Version to be published in JHE

Probing Neutralino Resonance Annihilation via Indirect Detection of Dark Matter

The lightest neutralino of R-parity conserving supersymmetric models serves as a compelling candidate to account for the presence of cold dark matter in the universe. In the minimal supergravity (mSUGRA) model, a relic density can be found in accord with recent WMAP data for large values of the parameter $\tan\beta$, where neutralino annihilation in the early universe occurs via the broad s-channel resonance of the pseudoscalar Higgs boson $A$. We map out rates for indirect detection of neutralinos via 1. detection of neutrinos arising from neutralino annihilation in the core of the earth or sun and 2. detection of gamma rays, antiprotons and positrons arising from neutralino annihilation in the galactic halo. If indeed $A$-resonance annihilation is the main sink for neutralinos in the early universe, then signals may occur in the gamma ray, antiproton and positron channels, while a signal in the neutrino channel would likely be absent. This is in contrast to the hyperbolic branch/focus point (HB/FP) region where {\it all} indirect detection signals are likely to occur, and also in contrast to the stau co-annihilation region, where {\it none} of the indirect signals are likely to occur.Comment: 12 pages including 4 eps figure

Direct Detection of Dark Matter in Supersymmetric Models

We evaluate neutralino-nucleon scattering rates in several well-motivated supersymmetric models, and compare against constraints on the neutralino relic density, BF( b\to s\gamma ) as well as the muon anomalous magnetic moment a_\mu . In the mSUGRA model, the indirect constraints favor the hyperbolic branch/focus point (HB/FP) region of parameter space, and in fact this region is just where neutralino-nucleon scattering rates are high enough to be detected in direct dark matter search experiments! In Yukawa unified SUSY SO(10) models with scalar mass non-universality, the relic density of neutralinos is almost always above experimental bounds, while the corresponding direct detection rates are below experimental levels. Conversely, in five dimensional SO(10) models where gauge symmetry breaking is the result of compactification of the extra dimension, and supersymmetry breaking is communicated via gaugino mediation, the relic density is quite low, while direct detection rates can be substantial.Comment: 25 page latex file including 18 EPS figures; revised version with references added and cross sections rescaled; figures changed. A copy of the paper with better resolution figures can be found at http://www.hep.fsu.edu/~belyaev/projects/directz1

La superación de profesores de matemática: un reto para la educación secundaria básica / The overcoming of mathematics teachers: a challenge for secondary school education

The knowledge society has caused profound transformations in all spheres, including education. This requires new ways of thinking and acting to develop an educational practice that responds to social demands. However, the increasing attention of teachers that is not satisfied with the graduations of universities and pedagogical schools constitutes a challenge. Another element to take into account is that many teachers only have comprehensive training without specialization in the subject. All these have as a result that teachers do not satisfy the needs of the school either quantitatively or qualitatively. Hence the importance of implementing processes of improvement that elevates the quality of their preparation so that teachers self-value their work in a positive sense and are appreciated by society. The work aims to characterize the improvement that teachers need based on their experience and opinions. To do this, a course is designed in a flexible way in which the teachers themselves identify their needs for improvement and reflection on its relevance.A sociedade do conhecimento trouxe transformações profundas em todas as esferas, incluindo a educação. Isto exige novas formas de pensar e agir a fim de desenvolver uma prática educativa que responda às exigências sociais. No entanto, a crescente falta de professores é um desafio que não é satisfeito com a graduação nas universidades e escolas pedagógicas. Outro elemento a ter em conta é que muitos professores só têm uma formação abrangente sem especialização de disciplinas. Como resultado, os professores não satisfazem as necessidades da escola, nem quantitativa nem qualitativamente. Daí a importância de implementar processos de melhoria que elevem a qualidade da sua preparação para que os professores possam valorizar o seu trabalho e ser devidamente apreciados pela sociedade. Este documento visa caracterizar a melhoria necessária para os professores com base na sua própria experiência e opiniões. Para este fim, um curso é concebido de uma forma flexível, em que os próprios professores identificam as suas próprias necessidades de melhoria e reflectem sobre a sua relevância.La sociedad del conocimiento ha provocado profundas trasformaciones en todas las esferas incluida la educación. Esto exige nuevas formas de pensar y actuar para desarrollar una práctica educativa que responda a las exigencias sociales. Sin embargo, constituye un reto la creciente carencia de profesores que no se satisface con las graduaciones de las universidades y escuelas pedagógicas. Además, los docentes en ejercicio no se sienten lo suficientemente valorados y consideran que su profesionalidad es cuestionada. Otro elemento a tener en cuenta es que muchos profesores solo cuentan con una formación integral sin especialización en la asignatura. Todo trae como resultado que los docentes no satisfacen ni cuantitativamente ni cualitativamente las necesidades de la escuela. De ahí la importancia de implementar procesos de superación que eleven la calidad de su preparación para que los docentes autovaloren su labor en sentido positivo y sean debidamente apreciados por la sociedad. El trabajo se propone caracterizar la superación que necesitan los docentes a partir de su propia experiencia y opiniones. Para ello se diseña un curso de forma flexible en el cual los propios profesores identifiquen sus necesidades de superación y reflexionen acerca de la pertinencia del mismo

Indirect, direct and collider detection of neutralino dark matter in the minimal supergravity model

We examine the prospects for supersymmetry discovery in the minimal supergravity (mSUGRA) model via indirect detection of neutralino dark matter. We investigate rates for muon detection in neutrino telescopes, and detection of photons, positrons and anti-protons by balloon and space based experiments. We compare the discovery reach in these channels with the reach for direct detection of dark matter, and also with the reach of collider experiments such as Fermilab Tevatron, CERN LHC and a ?s = 0.5–1 TeV linear e+e? collider. We pay particular attention to regions of model parameter space in accord with recent WMAP results on the dark matter density of the universe. We find that third generation direct dark matter detection experiments should be able to cover the entire WMAP allowed portion of the hyperbolic branch/focus point (HB/FP) region of parameter space, while the IceCube neutrino telescope can cover almost all this region. This is in contrast to the case of the CERN LHC or a linear e+e? collider, where only a fraction of the HB/FP region can be accessed. In addition, we show that detection of ?s, e+s and ¯ps should occur in much of the HB/FP region, as well as in the low m1/2 portion of the A annihilation funnel, and will be complementary to searches via colliders in these regions