Orbifold instantons, moment maps, and Yang-Mills theory with sources

We revisit the problem of constructing instantons on ADE orbifolds R4/Γ and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R4/Γ which are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kähler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically symmetric Γ-equivariant connections on complex V bundles over R4/Γ which are tailored to the way in which the orbifold group acts on the fibers. Some explicit Abelian and non-Abelian SU(2)-invariant solutions to the instanton equations on the orbifold are worked out. © 2013 American Physical Society

Application of PCR to a clinical and environmental investigation of a case of equine botulism

PCR for the detection of botulinum neurotoxin gene types A to E was used in the investigation of a case of equine botulism. Samples from a foal diagnosed with toxicoinfectious botulism in 1985 were reanalyzed by PCR and the mouse bioassay in conjunction with an environmental survey. Neurotoxin B was detected by mouse bioassay in culture enrichments of serum, spleen, feces, and intestinal contents. PCR results compared well with mouse bioassay results, detecting type B neurotoxin genes in these samples and also in a liver sample. Other neurotoxin types were not detected by either test. Clostridium botulinum type B was shown to be prevalent in soils collected from the area in which the foal was raised. Four methods were used to test for the presence of botulinum neurotoxin-producing organisms in 66 soil samples taken within a 5-km radius: PCR and agarose gel electrophoresis (types A to E), PCR and an enzyme-linked assay (type B), hybridization of crude alkaline cell lysates with a type B-specific probe, and the mouse bioassay (all types). Fewer soil samples were positive for C. botulinum type B by the mouse bioassay (15%) than by any of the DNA-based detection systems. Hybridization of a type B-specific probe to DNA dot blots (26% of the samples were positive) and PCR-enzyme-linked assay (77% of the samples were positive) were used for the rapid analysis of large numbers of samples, with sensitivity limits of 3 x 10(6) and 3,000 cells, respectively. Conventional detection of PCR products by gel electrophoresis was the most sensitive method (300-cell limit), and in the present environmental survey, neurotoxin B genes only were detected in 94% of the samples

QFT with Twisted Poincar\'e Invariance and the Moyal Product

We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.Comment: 11 pages, references adde

UV/IR duality in noncommutative quantum field theory

We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative Minkowski space.Comment: 12 pages; v2: minor corrections, note and references added; Contribution to proceedings of the 2nd School on "Quantum Gravity and Quantum Geometry" session of the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 13-20 2009. To be published in General Relativity and Gravitatio

Coordinate noncommutativity in strong non-uniform magnetic fields

Noncommuting spatial coordinates are studied in the context of a charged particle moving in a strong non-uniform magnetic field. We derive a relation involving the commutators of the coordinates, which generalizes the one realized in a strong constant magnetic field. As an application, we discuss the noncommutativity in the magnetic field present in a magnetic mirror.Comment: 4 page

Space-time non-commutativity tends to create bound states

We study the spectrum of fluctuations about static solutions in 1+1 dimensional non-commutative scalar field models. In the case of soliton solutions non-commutativity leads to creation of new bound states. In the case of static singular solutions an infinite tower of bound states is produced whose spectrum has a striking similarity to the spectrum of confined quark states.Comment: revtex4, 6 pages, v2: a reference adde

Towards an explicit expression of the Seiberg-Witten map at all orders

The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative parameter theta and the gauge potential A by the requirement that gauge orbits are mapped on gauge orbits. This of course leaves ambiguities, corresponding to gauge transformations, and there is an infinity of solutions. Is there one better, clearer than the others ? In the abelian case, we were able to find a solution, linked by a gauge transformation to already known formulas, which has the property of admitting a recursive formulation, uncovering some pattern in the map. In the special case of a pure gauge, both abelian and non-abelian, these expressions can be summed up, and the transformation is expressed using the parametrisation in terms of the gauge group.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physic

Cut-offs and pile-ups in shock acceleration spectra

We have examined cutoffs and pile-ups due to various processes in the spectra of particles produced by shock acceleration, and found that, even in the absence of energy losses, the shape of the spectrum of accelerated particles at energies well below the nominal maximum energy depends strongly on the energy dependence of the diffusion coefficient. This has implications in many areas, for example, in fitting the observed cosmic ray spectrum with models based on power-law source spectra and rigidity dependent diffusive escape from the galaxy. With continuous energy losses, prominent pile-ups may arise, and these should be included when modelling synchrotron X-ray and inverse Compton gamma-ray spectra from a shock-accelerated electron population. We have developed a Monte Carlo/numerical technique to model the shape of the spectrum for the case of non-continuous energy losses such as inverse Compton scattering in the Klein-Nishina regime. We find that the shapes of the resulting cut-offs differ substantially from those arising from continuous processes, and we suggest that such differences could be observable through their effect on the spectrum of radiation emitted by a population of recently accelerated electrons as, for example, may exist in young supernova remnants.Comment: 23 pages, 8 figures, submitted to Astroparticle Physic

(Non)commutative isotropization in Bianchi I with Barotropic perfect fluid and Λ\Lambda Cosmological

We present the classical solutions to the Einstein field equations derived using the WKB-like and Hamilton procedures. The investigation is carried out in the commutative and noncommutative scenario for the Bianchi type I cosmological model coupled to barotropic perfect fluid and $\lambda$ Cosmological for two different gauges. Noncommutativity is achieved by modifying the symplectic structure considering that all minisuperspace variables $\rm q^i$ does not commute and by a deformation between all the minisuperspace variables. In the gauge N=1, it is possible to obtain that the anisotropic parameter $\rm \beta_{\pm nc}$ tend to a constant curvature for large period of time considering different values in the noncommutative parameters $\theta$ and cosmological term. However, this behavior give the idea that is necessary introduce other class of matter in the models, for to have a real isotropization in the model, such as dark energy or dark matter.Comment: 15 pages, 1 figur