The Open String Regge Trajectory and Its Field Theory Limit

We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multi-loop diagrams describes the 't Hooft limit N\to\infty. Our motivation is to improve the understanding of open string theory at finite \alpha' as a model of gauge theories. SU(N) gauge theories in D space-time dimensions are described by requiring open strings to end on a stack of N Dp-branes of space-time dimension D=p+1. The large N leading trajectory \alpha(t)=1+\alpha' t+\Sigma(t) can be extracted, through order g^2, from the s\to-\infty limit, at fixed t, of the four open string tree and planar loop diagrams. We analyze the t\to0 behavior with the result that \Sigma(t)\sim-Cg^2(-\alpha' t)^{(D-4)/2}/(D-4). This result precisely tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D\to4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -\ln(-\alpha^\prime t). We also study \Sigma(t) in the limit t\to-\infty and show that, when D<8, it behaves as \alpha^\prime t/(\ln(-\alpha^\prime t))^{\gamma}, where \gamma>0 depends on D and the number of massless scalars. Thus, as long as 4<D<8, the 1-loop correction stays small relative to the tree trajectory for the whole range -\infty<t<0. Finally we present the results of numerical calculations of \Sigma(t) for all negative t.Comment: 19 pages, 5 figure

Heating of ions by low-frequency Alfv\'{e}n waves in partially ionized plasmas

In the solar atmosphere, the chromospheric and coronal plasmas are much hotter than the visible photosphere. The heating of the solar atmosphere, including the partially ionized chromosphere and corona, remains largely unknown. In this paper we demonstrate that the ions can be substantially heated by Alfv\'{e}n waves with very low frequencies in partially ionized low beta plasmas. This differs from other Alfv\'{e}n wave related heating mechanisms such as ion-neutral collisional damping of Alfv\'{e}n waves and heating described by previous work on resonant Alfv\'{e}n wave heating. In this paper, we find that the non-resonant Alfv\'{e}n wave heating is less efficient in partially ionized plasmas than when there are no ion-neutral collisions, and the heating efficiency depends on the ratio of the ion-neutral collision frequency to the ion gyrofrequency.Comment: Published as Letter

Ducted compressional waves in the magnetosphere in the double-polytropic approximation

International audienceSmall-amplitude compressional magnetohydrodynamic-type waves are studied in the magnetosphere. The magnetosphere is treated as a rarefied plasma with anisotropy in the kinetic pressure distribution. The parallel and perpendicular pressures are defined by general polytropic pressure laws. This double-polytropic model can be considered as a natural extension of the magnetohydrodynamic (MHD) model when the plasma is collisionless. Generalized dispersion relations for surface and body waves are derived and analyzed for an isolated magnetic slab. The waves are confined to the slab. For specific polytropic indices, the results obtained in the (i) Chew-Goldberger-Low (CGL) double-adiabatic and (ii) double-isothermal approximations are recovered

Solar feature tracking in both spatial and temporal domains

A new method for automated coronal loop tracking, in both spatial and temporal domains, is presented. The reliability of this technique was tested with TRACE 171A observations. The application of this technique to a flare-induced kink-mode oscillation, revealed a 3500 km spatial periodicity which occur along the loop edge. We establish a reduction in oscillatory power, for these spatial periodicities, of 45% over a 322 s interval. We relate the reduction in oscillatory power to the physical damping of these loop-top oscillations

The effect of twisted magnetic field on the resonant absorption of MHD waves in coronal loops

The standing quasi modes in a cylindrical incompressible flux tube with magnetic twist that undergoes a radial density structuring is considered in ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae, the dispersion relation for the MHD waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was found that a magnetic twist will increase the frequencies, damping rates and the ratio of the oscillation frequency to the damping rate of these modes. The period ratio P_1/P_2 of the fundamental and its first-overtone surface waves for kink (m=1) and fluting (m=2,3) modes is lower than 2 (the value for an untwisted loop) in the presence of twisted magnetic field. For the kink modes, particularly, the magnetic twists B_{\phi}/B_z=0.0065 and 0.0255 can achieve deviations from 2 of the same order of magnitude as in the observations. Furthermore, for the fundamental kink body waves, the frequency bandwidth increases with increasing the magnetic twist.Comment: 18 pages, 9 figure

Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors

Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved spacetime. In the framework of zeta function regularization, we find the one-loop effective action to all orders in the magnetic field up to linear terms in the Riemannian curvature. As a particular case, we also obtain the one-loop effective action for massless scalar and spinor fields. In this setting, we found that the vacuum energy of charged spinors with small mass becomes very large due entirely by the gravitational correction.Comment: LaTeX, 23 page

Anomalous biased diffusion in a randomly layered medium

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws and analyze their dependence on the particle mass and the distribution of the random force.Comment: 19 pages, 1 figur