Related papers: Nineteen vortex equations and integrability
The Taubes equation for Abelian Higgs vortices is generalised to five distinct U(1) vortex equations. These include the Popov and Jackiw--Pi vortex equations, and two new equations. The Baptista metric, a conformal rescaling of the…
The five integrable vortex equations, recently studied by Manton, are generalized to include magnetic impurities of the Tong-Wong type. Under certain conditions these generalizations remain integrable. We further set up a gauge theory with…
The first half of the thesis concerns Abelian vortices and Yang-Mills (YM) theory. It is proved that the 5 types of vortices recently proposed by Manton are symmetry reductions of (A)SDYM equations with suitable gauge groups and symmetry…
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…
The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term.…
We study BPS vortices in the mass-deformed non-relativistic ${\C N}=6$ $U(N)_k\times U(N)_{-k}$ Chern-Simons-matter theory. We focus on the massive deformation that preserves the maximal ${\C N}=6$ supersymmetry, and consider a…
An analytic method to calculate the vortex number on a torus is constructed, focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose governing equation is the so-called Jackiw-Pi equation. The equation is one of the…
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…
Existence of Maxwell-Chern-Simons-Higgs (MCSH) vortices in a Hermitian line bundle $\L$ over a general compact Riemann surface $\Sigma$ is proved by a continuation method. The solutions are proved to be smooth both spatially and as…
We investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. We systematically classify the BPS equations in terms of the number of supersymmetry and the R-symmetries of the undeformed and mass-deformed…
We demonstrate that the five vortex equations recently introduced by Manton ariseas symmetry reductions of the anti-self-dual Yang--Mills equations in four dimensions. In particular the Jackiw--Pi vortex and the Ambj\o rn--Olesen vortex…
We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the…
We present a (2+1)-dimensional gauged $O(3) \sigma$-model with an Abelian Chern--Simons term. It shows topologically stable, anyonic vortices as classical solutions. The fields are studied in the case of rotational symmetry and analytic…
An infinite family of integrable vortex equations is studied and related to the Cartan geometry of the underlying Riemann surfaces. This Cartan picture gives an interpretation of the vortex equations as the flatness of a non-Abelian…
In this work we propose a parity-invariant Maxwell-Chern-Simons $U(1) \times U(1)$ model coupled with two charged scalar fields in $2+1$ dimensions, and show that it admits finite-energy topological vortices. We describe the main features…
We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction…
We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions…
We focus on BPS solutions of the gauged O(3) Sigma model, due to Schroers, and use these ideas to study the geometry of the moduli space. The model has an asymmetry parameter $\tau$ breaking the symmetry of vortices and antivortices on the…
A consistent BPS formalism to study the existence of topological axially symmetric vortices in generalized versions of the Born-Infeld-Higgs electrodynamics is implemented. Such a generalization modifies the field dynamics via introduction…
We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1} \times T^2 with Nf=Nc…