Low-Energy Dynamics of String Solitons

The dynamics of a class of fivebrane string solitons is considered in the moduli space approximation. The metric on moduli space is found to be flat. This implies that at low energies the solitons do not interact, and their scattering is trivial. The range of validity of the approximation is also briefly discussed.Comment: 8 pages, Minor typos correcte

Static intervortex forces

A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca theory) in the presence of a singular point source at the vortex centre. It is shown that this source is a composite scalar monopole and magnetic dipole, and the respective charges are determined numerically for various values of the coupling constant. The interaction potential of two well separated vortices is computed by calculating the interaction Lagrangian of two such point sources in the linear theory. The potential is used to model type II vortex scattering.Comment: Much shorter (10 pages) published version, new titl

More on scattering of Chern-Simons vortices

I derive a general formalism for finding kinetic terms of the effective Lagrangian for slowly moving Chern-Simons vortices. Deformations of fields linear in velocities are taken into account. From the equations they must satisfy I extract the kinetic term in the limit of coincident vortices. For vortices passing one over the other there is locally the right-angle scattering. The method is based on analysis of field equations instead of action functional so it may be useful also for nonvariational equations in nonrelativistic models of Condensed Matter Physics.Comment: discussion around Eq.(45) is generalised, one more condition for the local right-angle scattering is adde

A Quantum Hall Fluid of Vortices

In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of the quantum Hall droplet. As the number of vortices becomes large, they fill the plane and a hydrodynamic treatment becomes possible, resulting in the non-commutative theory of Susskind. Key to the story is the recent D-brane realisation of vortices and their moduli spaces.Comment: 10 pages. v2(3): (More) References adde

Expansion for the solutions of the Bogomolny equations on the torus

We show that the solutions of the Bogomolny equations for the Abelian Higgs model on a two-dimensional torus, can be expanded in powers of a quantity epsilon measuring the departure of the area from the critical area. This allows a precise determination of the shape of the solutions for all magnetic fluxes and arbitrary position of the Higgs field zeroes. The expansion is carried out to 51 orders for a couple of representative cases, including the unit flux case. We analyse the behaviour of the expansion in the limit of large areas, in which case the solutions approach those on the plane. Our results suggest convergence all the way up to infinite area.Comment: 26 pages, 8 figures, slightly revised version as published in JHE

EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory

We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the non-existence of absolute time resp. simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution $\rho = |\psi |^2$ cannot simultaneously be realized in all Lorentz frames of reference.Comment: 24 pages, LaTex, 4 figure

Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.Comment: 22 pages, 2 figures, JHEP3 style. v2: This paper is a thoroughly revised version. We thank P.A. Horvathy, L. Martina and P.C. Stichel for illuminating comments that led us to reconsider some of our previously reported results; see note added at the end of the paper. v3: Acknowledgements adde

First and Second Order Vortex Dynamics

The low energy dynamics of vortices in selfdual Abelian Higgs theory is of second order in vortex velocity and characterized by the moduli space metric. When Chern-Simons term with small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provides an additional check of the first and second order terms by studying the angular momentum in the field theory. We briefly explore other first order term due to small background electric charge density and also the harmonic potential well for vortices given by the moment of inertia.Comment: a rev tex file, 22 pages, no figur

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure

Low Energy Nucleon-Nucleon Scattering with the Skyrme Model in the Geodetic Approximation

We calculate nucleon-nucleon scattering at low energies and large impact parameter in the Skyrme model within the framework for soliton scattering proposed by Manton. This corresponds to a truncation of the degrees of freedom to the twelve collective coordinates which essentially describe the rigid body motion of the pair of Skyrmions. We take to its logical conclusion the result that the induced kinetic energy for these collective coordinates in the product ansatz behaves as one over the separation and hence can dominate over the potential. This behaviour implies to leading order that we can drop the potential and the resulting motion reduces simply to geodesic motion on the manifold parametrized by the variables of the product ansatz. We formulate the semi-classical quantization of these variables to obtain the motion corresponding to the nucleonic states of the Skyrme model. This is the appropriate description for the nucleons in order to consider their scattering within Manton's framework in the semi-classical approximation. We investigate the implications for the scattering of nucleons with various initial polarizations using the approximation method of ``variation of constants''.Comment: 18 pages, UDEM-LPN-TH-94-19