Noncommutative Electrodynamics with covariant coordinates

We study Noncommutative Electrodynamics using the concept of covariant coordinates. We propose a scheme for interpreting the formalism and construct two basic examples, a constant field and a plane wave. Superposing these two, we find a modification of the dispersion relation. Our results differ from those obtained via the Seiberg-Witten map.Comment: 5 pages, published versio

Neuronal avalanches recorded in the awake and sleeping monkey do not show a power law but can be reproduced by a self-organized critical model

Poster presentation: Self-organized critical (SOC) systems are complex dynamical systems that may express cascades of events, called avalanches [1]. The SOC state was proposed to govern brain function, because of its activity fluctuations over many orders of magnitude, its sensitivity to small input and its long term stability [2,3]. In addition, the critical state is optimal for information storage and processing [4]. Both hallmark features of SOC systems, a power law distribution f(s) for the avalanche size s and a branching parameter (bp) of unity, were found for neuronal avalanches recorded in vitro [5]. However, recordings in vivo yielded contradictory results [6]. Electrophysiological recordings in vivo only cover a small fraction of the brain, while criticality analysis assumes that the complete system is sampled. We hypothesized that spatial subsampling might influence the observed avalanche statistics. In addition, SOC models can have different connectivity, but always show a power law for f(s) and bp = 1 when fully sampled. This may not be the case under subsampling, however. Here, we wanted to know whether a state change from awake to asleep could be modeled by changing the connectivity of a SOC model without leaving the critical state. We simulated a SOC model [1] and calculated f(s) and bp obtained from sampling only the activity of a set of 4 × 4 sites, representing the electrode positions in the cortex. We compared these results with results obtained from multielectrode recordings of local field potentials (LFP) in the cortex of behaving monkeys. We calculated f(s) and bp for the LFP activity recorded while the monkey was either awake or asleep and compared these results to results obtained from two subsampled SOC model with different connectivity. f(s) and bp were very similar for both the experiments and the subsampled SOC model, but in contrast to the fully sampled model, f(s) did not show a power law and bp was smaller than unity. With increasing the distance between the sampling sites, f(s) changed from "apparently supercritical" to "apparently subcritical" distributions in both the model and the LFP data. f(s) and bp calculated from LFP recorded during awake and asleep differed. These changes could be explained by altering the connectivity in the SOC model. Our results show that subsampling can prevent the observation of the characteristic power law and bp in SOC systems, and misclassifications of critical systems as sub- or supercritical are possible. In addition, a change in f(s) and bp for different states (awake/asleep) does not necessarily imply a change from criticality to sub- or supercriticality, but can also be explained by a change in the effective connectivity of the network without leaving the critical state

Supersymmetric D2 anti-D2 Strings

We consider the flat supersymmetric D2 and anti-D2 system, which follows from ordinary noncommutative D2 anti-D2 branes by turning on an appropriate worldvolume electric field describing dissolved fundamental strings. We study the strings stretched between D2 and anti-D2 branes and show explicitly that the would-be tachyonic states become massless. We compute the string spectrum and clarify the induced noncommutativity on the worldvolume. The results are compared with the matrix theory description of the worldvolume gauge theories

Elliptic supertube and a Bogomol'nyi-Prasad-Sommerfield D2-brane--anti-D2-brane Pair

An exact solution, in which a D2-brane and an anti-D2-brane are connected by an elliptically tubular D2-brane, is obtained without any junction condition. The solution is shown to preserve one quarter of the supersymmetries of the type-IIA Minkowski vacuum. We show that the configuration cannot be obtained by "blowing-up" from some inhomogeneously D0-charged superstrings. The BPS bound tells us that it is rather composed of D0-charged D2-brane-anti-D2-brane pair and a strip of superstrings connecting them. We obtain the correction to the charges of the string end points in the constant magnetic background.Comment: v3. 12 pages, journal version; title changed, length trimmed to fit for Rapid Communication forma

Radiation Damping of a BPS Monopole; an Implication to S-duality

The radiation reaction of a BPS monopole in the presence of incident electromagnetic waves as well as massless Higgs waves is analyzed classically. The reactive forces are compared to those of $W$ boson that is interpreted as a dual partner of the BPS monopole. It is shown that the damping of acceleration is dual to each other, while in the case of finite size effects the duality is broken explicitly. Their implications on the duality are discussed.Comment: 20 pages, uses revtex, changes in reference

Covariant Coordinate Transformations on Noncommutative Space

We show how to define gauge-covariant coordinate transformations on a noncommuting space. The construction uses the Seiberg-Witten equation and generalizes similar results for commuting coordinates.Comment: 11 pages, LaTeX; email correspondence to [email protected]

Self-organisation to criticality in a system without conservation law

We numerically investigate the approach to the stationary state in the nonconservative Olami-Feder-Christensen (OFC) model for earthquakes. Starting from initially random configurations, we monitor the average earthquake size in different portions of the system as a function of time (the time is defined as the input energy per site in the system). We find that the process of self-organisation develops from the boundaries of the system and it is controlled by a dynamical critical exponent z~1.3 that appears to be universal over a range of dissipation levels of the local dynamics. We show moreover that the transient time of the system $t_{tr}$ scales with system size L as $t_{tr} \sim L^z$. We argue that the (non-trivial) scaling of the transient time in the OFC model is associated to the establishment of long-range spatial correlations in the steady state.Comment: 10 pages, 6 figures; accepted for publication in Journal of Physics

Counting Yang-Mills Dyons with Index Theorems

We count the supersymmetric bound states of many distinct BPS monopoles in N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here is that we work in generic Coulombic vacua where more than one adjoint Higgs fields are turned on. The number of purely magnetic bound states is again found to be consistent with the electromagnetic duality of the N=4 SU(n) theory, as expected. We also count dyons of generic electric charges, which correspond to 1/4 BPS dyons in N=4 theories and 1/2 BPS dyons in N=2 theories. Surprisingly, the degeneracy of dyons is typically much larger than would be accounted for by a single supermultiplet of appropriate angular momentum, implying many supermutiplets of the same charge and the same mass.Comment: 34 pages, 1 figure, LaTe

Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory

We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4 supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation values are turned on. When only one Higgs is turned on, the Lagrangian is purely kinetic. When all six are turned on, however, this moduli space dynamics is augmented by five independent potential terms, each in the form of half the squared norm of a Killing vector field on the moduli space. A generic stationary configuration of the monopoles can be interpreted as stable non BPS dyons, previously found as non-planar string webs connecting D3-branes. The supersymmetric extension is also found explicitly, and gives the complete quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR

Melting of hexagonal skyrmion states in chiral magnets

Skyrmions are spiral structures observed in thin films of certain magnetic materials (Uchida et al 2006 Science 311 359–61). Of the phases allowed by the crystalline symmetries of these materials (Yi et al 2009 Phys. Rev. B 80 054416), only the hexagonally packed phases (SCh) have been observed. Here the melting of the SCh phase is investigated using Monte Carlo simulations. In addition to the usual measure of skyrmion density, chiral charge, a morphological measure is considered. In doing so it is shown that the low-temperature reduction in chiral charge is associated with a change in skyrmion profiles rather than skyrmion destruction. At higher temperatures, the loss of six-fold symmetry is associated with the appearance of elongated skyrmions that disrupt the hexagonal packing