Remarks on charged vortices in the Maxwell–Chern–Simons model (original) (raw)

Electrically and magnetically charged vortices in the Chern–Simons–Higgs theory

2009

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern-Simons-Higgs theory for which both the Maxwell term and Chern-Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern-Simons term.

Comment on vortices in Chern-Simons and Maxwell electrodynamics with Higgs fields

Physics Letters B, 1994

We compare the vortex-like solutions of two different theories in (2 + 1) dimensions. In the first a nonrelativistic field self-interacts through a Chern-Simons gauge connection. It is P and T violating. The second is the standard Maxwell scalar electrodynamics. We show that for specific values of some parameters the same vortex-configurations provide solutions for both theories.

Chern–Simons vortices in the Gudnason model

Journal of Functional Analysis, 2014

We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the N = 2 supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern-Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an-inequality constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges.

Vortices in a nonminimal Maxwell Chern-Simons O(3) sigma model

Physics Letters B

In this work we consider an Abelian O(3) sigma model coupled nonminimally with a gauge field governed by Maxwell and Chern–Simons terms. Bogomol'nyi equations are constructed for a specific form of the potential and generic nonminimal coupling constant. Furthermore, topological and nontopological self-dual soliton solutions are obtained for a critical value of the nonminimal coupling constant. Some particular static vortex solutions (topological and nontopological) satisfying the Bogomol'nyi bound are numerically solved and presented.

Vortices in (Abelian) Chern–Simons gauge theory

Physics Reports, 2009

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. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation.

BPS Vortices with Negative Electric Charge in The Generalized Maxwell-Chern-Simons-Higgs Model

2021

In this paper we show how rederive the Bogomolny’s equations of generalized Maxwell-ChernSimons-Higgs model presented in Ref. [1] by using BPS Lagrangian method. We also show that the other results (identification, potential terms, Gauss’s law constraint) in there can be obtained rigorously with a particular form of the BPS Lagrangian density. In this method, we find that the potential terms are the most general form that could have the BPS vortex solutions. The Gauss’s law constraint turns out to be the Euler-Lagrange equations of the BPS Lagrangian density. We also find another BPS vortex solutions by taking other identification between the neutral scalar field and the electric scalar potential field, N = ±A0, which is different by a relative sign to the identification in Ref. [1], N = ∓A0,. We find the BPS vortex solutions have negative electric charge which are related to the corresponding BPS vortes solutions in Ref. [1] by tranforming the neutral scalar field N → −N . Other po...

BPS Maxwell-Chern-Simons-Like Vortices in a Lorentz-Violating Framework

CPT and Lorentz Symmetry, 2014

We have analyzed Maxwell-Chern-Simons-Higgs BPS vortices in a Lorentzviolating CPT-odd context. The Lorentz violation induces profiles with a conical behavior at the origin. For some combination of the coefficients for Lorentz violation there always exists a sufficiently large winding number for which the magnetic field flips its sign.