Related papers: Five Vortex Equations
The class of five integrable vortex equations discussed recently by Manton is extended so it includes the relativistic BPS Chern-Simons vortices, yielding a total of nineteen vortex equations. Not all the nineteen vortex equations are…
It is shown that both the sinh--Gordon equation and the elliptic Tzitzeica equation can be interpreted as the Taubes equation for Abelian vortices on a CMC surface embedded in $\R^{2, 1}$, or on a surface conformally related to a hyperbolic…
The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol'nyi-type bound. We examine cylindrically…
Popov recently discovered a modified version of the Bogomolny equations for abelian Higgs vortices, and showed they were integrable on a sphere of curvature 1/2. Here we construct a large family of explicit solutions, where the vortex…
Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle…
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as…
We construct an extension of the Abelian Higgs model, which consists of a complex scalar field by including an additional real, electromagnetically neutral scalar field. We couple this real scalar field to the complex scalar field via a…
The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background.…
We study vortex solutions in a theory with dynamics governed by two weakly coupled Abelian Higgs models, describing a hidden sector and a visible sector. We analyze the radial dependence of the axially symmetric solutions constructed…
The excitations of the vortex in Abelian Higgs model with small ratio of vector and Higgs particle masses are considered. Three main modes encountered in numerical computations are described in detail. They are also compared to analytic…
Vortices represent a class of topological solitons arising in gauge theories coupled with complex scalar fields, holding significant importance across various domains of modern physics. In this paper we establish the existence of vortex…
We consider a single Abelian Higgs vortex on a surface {\Sigma} whose Gaussian curvature K is small relative to the size of the vortex, and analyse vortex motion by using geodesics on the moduli space of static solutions. The moduli space…
We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class…
We consider the Abelian-Higgs model with two complex scalar fields and arbitrary positive integer charges with the addition of a higher-order generalization of the Josephson term. The theory possesses vortices of both local and global…
We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given…
The thermodynamics of vortices in the critically coupled abelian Higgs model, defined on the plane, are investigated by placing $N$ vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli…
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that…
We consider the vortex equations for a U(n) gauge field coupled to a Higgs field with values on the n times n square matrices. It is known that when these equations are defined on a compact Riemann surface, their moduli space of solutions…
Following a brief review of known vortex solutions in SU(N) gauge-adjoint Higgs theories we show the existence of a new ``minimal'' vortex solution in SU(3) gauge theory with two adjoint Higgs bosons. At a critical coupling the vortex…
Classical vortex solutions in various two-Higgs systems are studied. The systems we consider include the standard model with two Higgs doublets, in which case the vortex appears as part of a string-like object. The Higgs potentials contain…