On self-dual Yang-Mills fields on special complex surfaces

We derive a generalization of the flat space Yang's and Newman's equations for self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian 4-manifolds. The results also apply to Einstein metrics (whose full curvature is not necessarily self-dual). We analyse the possibility of hidden symmetries in the form of Backlund transformations, and we find a continuous group of hidden symmetries only for the case in which the geometry is conformally half-flat. No isometries are assumed

Conformal geometry and half-integrable spacetimes

Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4-dimensional closed Einstein-Weyl structures which are half-algebraically special and admit a "half-integrable" almost-complex structure. That is, we reduce the Einstein-Weyl equations to a single, conformally invariant, non-linear scalar equation, that we call the "conformal HH equation", and we reconstruct the conformal structure (curvature and metric) from a solution to this equation. We show that the conformal metric is composed of: a conformally flat part, a conformally half-flat part related to certain "constants" of integration, and a potential part that encodes the full non-linear curvature, and that coincides in form with the Hertz potential from perturbation theory. We also study the potentialization of the Dirac-Weyl, Maxwell (with and without sources), and Yang-Mills systems. We show how to deal with the ordinary Einstein equations by using a simple trick. Our results give a conformally invariant, coordinate-free, generalization of the hyper-heavenly construction of Plebanski and collaborators

Double field theory, twistors, and integrability in 4-manifolds

The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be understood in terms of generalized geometry and, more recently, para-Hermitian geometry. In this work we apply techniques associated to this doubled geometry to four-dimensional manifolds, and we show that they are particularly well-suited to the analysis of integrability in special spacetimes, especially in connection with Penrose's twistor theory and its applications to general relativity. This shows a close relationship between some of the geometrical structures in the para-Hermitian approach to double field theory and those in algebraically special solutions to the Einstein equations. Particular results include the classification of four-dimensional, possibly complex-valued, (para-)Hermitian structures in different signatures, the Lie and Courant algebroid structures of special spacetimes, and the analysis of deformations of (para-)complex structures. We also discuss a notion of "weighted algebroids" in relation to a natural gauge freedom in the framework. Finally, we analyse the connection with two- and three-dimensional (real and complex) twistor spaces, and how the former can be understood in terms of the latter, in particular in terms of twistor families

Parallel spinors, pp-waves, and gravitational perturbations

We prove that any real, vacuum gravitational perturbation of a 4-dimensional vacuum pp-wave space-time can be locally expressed, modulo gauge transformations, as the real part of a Hertz/Debye potential, where the scalar potential satisfies the wave equation. We discuss relations with complex perturbations, complex space-times, non-linear structures, and real spaces with split (ultra-hyperbolic/Kleinian) signature. Motivated by generalized notions of parallel spinors, we also discuss generalizations of the result to other space-times

Kaehler geometry of black holes and gravitational instantons

We obtain a closed formula for the Kaehler potential of a broad class of four-dimensional Lorentzian or Euclidean conformal "Kaehler" geometries, including the Plebanski-Demianski class and various gravitational instantons such as Fubini-Study and Chen-Teo. We show that the Kaehler potentials of Schwarzschild and Kerr are related by a Newman-Janis shift. Our method also shows that a class of supergravity black holes, including the Kerr-Sen spacetime, is Hermitian (but not conformal Kaehler). We finally show that the integrability conditions of complex structures lead naturally to the (non-linear) Weyl double copy, and we give new vacuum and non-vacuum examples of this relation

On the geometry of Petrov type II spacetimes

In general, geometries of Petrov type II do not admit symmetries in terms of Killing vectors or spinors. We introduce a weaker form of Killing equations which do admit solutions. In particular, there is an analog of the Penrose-Walker Killing spinor. Some of its properties, including associated conservation laws, are discussed. Perturbations of Petrov type II Einstein geometries in terms of a complex scalar Debye potential yield complex solutions to the linearized Einstein equations. The complex linearized Weyl tensor is shown to be half Petrov type N. The remaining curvature component on the algebraically special side is reduced to a first order differential operator acting on the potential

Pure single photons from a trapped atom source

Single atoms or atom-like emitters are the purest source of on-demand single photons, they are intrinsically incapable of multi-photon emission. To demonstrate this degree of purity we have realized a tunable, on-demand source of single photons using a single ion trapped at the common focus of high numerical aperture lenses. Our trapped-ion source produces single-photon pulses at a rate of 200 kHz with g$^2(0) = (1.9 \pm 0.2) \times 10^{-3}$, without any background subtraction. The corresponding residual background is accounted for exclusively by detector dark counts. We further characterize the performance of our source by measuring the violation of a non-Gaussian state witness and show that its output corresponds to ideal attenuated single photons. Combined with current efforts to enhance collection efficiency from single emitters, our results suggest that single trapped ions are not only ideal stationary qubits for quantum information processing, but promising sources of light for scalable optical quantum networks.Comment: 7 pages plus one page supplementary materia

Evaluation of the viability of bee eggs Apis mellifera L. when submited to ultra-violet radiation.

En esta investigación se evaluó la viabilidad de huevos de Apis mellifera L. expuestos a radiación UV-A y UV-B mediante un tubo fluorescente con espectro entre los 280 nm a los 720 nm de 30 watts de potencia. El diseño experimental fue completamente al azar evaluándose viabilidad con tiempos de exposición de 0 s, 10 s, 30 s, 60 s y 90 s. El método de evaluación fue la presencia de celdillas operculadas al noveno día después de exponer los huevos de 24 horas a radiación. Los resultados obtenidos de las medias entre los distintos tiempos de exposición demostraron que existen diferencias estadísticamente significativas entre los tratamientos. Se presentó una mayor viabilidad a 0 s con 89,26%, para 10 s de exposición 56,59%, para 30 s 36,47%, para 60 s 31,46% y para 90 s de exposición 21,83% de viabilidad. Con este experimento se obtienen valiosos antecedentes sobre los cuales trabajar a fin de reducir pérdidas en crías de abejas, las cuales son sensibles a exposiciones de radiación UV.This study evaluated the viability of the eggs of Apis mellifera L. (honeybee) when exposed to UV-A and UV-B radiation using a fluorescent tube of 30 watts power with a spectrum between 280 nm and 720 nm. The design of the experiment was completely random, with evaluations of viability after exposure times of 0, 10, 30, 60 and 90 seconds. The evaluation method was the presence of operculate cells on the ninth day after exposure of 24-hour old eggs to radiation. The results obtained from the measurements among the different exposure times showed that there were statistically significant differences between the treatments. The greatest viability occurred at 0 exposure with 89.26%, followed by 56.59% for 10 s exposure, 36.47% for 30 s, 31.46% for 60 s, and 21.83% viability with 90 s exposure,. This experiment provides valuable information with which to reduce bee losses in breeding programmes, since they are sensitive to exposure to UV radiation