209 research outputs found

    Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry

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    We study the nonlinear σ\sigma-model in an external magnetic field applied on curved surfaces with rotational symmetry. The Euler-Lagrange equations derived from the Hamiltonian yield the double sine-Gordon equation (DSG) provided the magnetic field is tuned with the curvature of the surface. A 2π2\pi skyrmion appears like a solution for this model and surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. We also study some specific examples by applying the model on three rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. The coupling between a magnetic field and the curvature of the substract is an interesting result and we believe that this issue may be relevant to be applied in condensed matter systems, e.g., superconductors, nematic liquid crystals, graphene and topological insulators.Comment: To be published in Physics Letters

    Born-Infeld particles and Dirichlet p-branes

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    Born-Infeld theory admits finite energy point particle solutions with δ\delta-function sources, BIons. I discuss their role in the theory of Dirichlet pp-branes as the ends of strings intersecting the brane when the effects of gravity are ignored. There are also topologically non-trivial electrically neutral catenoidal solutions looking like two pp-branes joined by a throat. The general solution is a non-singular deformation of the catenoid if the charge is not too large and a singular deformation of the BIon solution for charges above that limit. The intermediate solution is BPS and Coulomb-like. Performing a duality rotation we obtain monopole solutions, the BPS limit being a solution of the abelian Bogolmol'nyi equations. The situation closely resembles that of sub and super extreme black-brane solutions of the supergravity theories. I also show that certain special Lagrangian submanifolds of Cp{\Bbb C}^p, p=3,4,5p=3,4,5, may be regarded as supersymmetric configurations consisting of pp-branes at angles joined by throats which are the sources of global monopoles. Vortex solutions are also exhibited.Comment: 40 pages Latex file, no figure

    On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

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    We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and π\pi-solitons are predicted. The second one is given by the XY model, leading to a vortex turning around the surface. Helical states are also considered, however, topological arguments can not be used to ensure its stability. The energy and the anisotropy parameter which stabilizes the vortex state are explicitly calculated for two surfaces: catenoid and hyperboloid. The results show that the anisotropy and the vortex energy depends on the underlying geometry.Comment: 10 pages, 2 figures, Accepted for publication in Phys. Lett A (2013

    D-Branes and their Absorptivity in Born-Infeld Theory

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    Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born-Infeld theory. In particular the equation of small fluctuations about the D-brane is derived and converted into a modified Mathieu equation and - complementing earlier low-energy investigations in the case of the dilaton-axion system - studied in the high-energy domain. Explicit expressions are derived for the S-matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.Comment: latex, 26 pages, 4 figures, one reference added, to appear in Nucl. Phys.

    A Note on Tachyons in the D3+D3ˉD3+{\bar {D3}} System

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    The periodic bounce of Born-Infeld theory of D3D3-branes is derived, and the BPS limit of infinite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born--Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3: explanations and references added. Final version to appear in Mod. Phys. Lett.
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