Chern Simons Higgs Model Research Articles

Complete solvability of the time dependent self-dual equations Of Chern—Simons—Higgs model

Complete solvability of the time dependent self-dual equations Of Chern—Simons—Higgs model

Topological multi-vortex solutions of the Maxwell–Chern–Simons–Higgs model with a background metric

In this paper, we consider the self-dual equations arising from the Maxwell–Chern–Simons–Higgs model in a curved space with a background metric (1,−b(x),−b(x)). We assume that b(x) is not a constant and decays like |x|−γ with γ∈(0,2). Then, we prove that there exists a positive constant β∗ such that we have a topological solution of the self-dual equations if the couplings constants κ and q satisfy κq>β∗. We also verify the Chern–Simons limit which means that our solutions converge to the solution of the self-dual Chern–Simons vortex equation as q→∞.

The asymptotic behavior of Chern–Simons Vortices for Gudnason Model

We consider an elliptic system arising from a supersymmetric gauge field theory. In this paper, we complete to classify all possible solutions according to their asymptotic behavior under a weak coupling effect. Interestingly, it turns out that one of components does not follow the feature of condensate solutions for the classical Chern–Simons–Higgs model. Moreover, in order to prove the concentration property of blow up component, we need to improve the convergence rate and the gradient estimation for the other component, which converges to a constant. We expect that this result would provide an insight for the study of general elliptic system problems, which are even neither cooperative nor competitive.

Existence of radial solutions in the Chern–Simons–Higgs model with its SUSY extension

In this paper, we study a system of elliptic equations in which arises from the abelian Chern–Simons–Higgs theory and its SUSY extension. This system is expected to have three types of solutions: topological solutions, mixed type solutions and non-topological solutions. We establish the existence of the radial solutions of these three types.

L∞ bounds for Chern–Simons gauged equations in R1+1 and their applications

We estimate the L∞ norm of the first derivative of the solution to the Chern–Simons gauged O(3) sigma model in R1+1 by using local energy conservation and observing the transport equation along the characteristic line. As an application of the bound, we improve the growth rate of the H2 norm of the solution from an exponential to a polynomial one. We also apply a similar idea to the Chern–Simons–Higgs model.

Compactness, existence and multiplicity for the singular mean field problem with sign-changing potentials

In this paper we consider a mean field problem on a compact surface without boundary in presence of conical singularities. The corresponding equation, named after Liouville, appears in the Gaussian curvature prescription problem in Geometry, and also in the Electroweak Theory and in the abelian Chern–Simons–Higgs model in Physics. Our contribution focuses on the case of sign-changing potentials, and gives results on compactness, existence and multiplicity of solutions.

Existence theorems for non-Abelian Chern–Simons–Higgs vortices with flavor

In this paper we establish the existence of vortex solutions for a Chern–Simons–Higgs model with gauge group SU(N)×U(1) and flavor SU(N). These symmetries ensure the existence of genuine non-Abelian vortices through a color–flavor locking. Under a suitable ansatz we reduce the problem to a 2×2 system of nonlinear elliptic equations with exponential terms. We study this system over the full plane and over a doubly periodic domain, respectively. For the planar case we use a variational argument to establish the existence result and derive the decay estimates of the solutions. Over the doubly periodic domain we show that the system admits at least two gauge-distinct solutions carrying the same physical energy by using a constrained minimization approach and the mountain-pass theorem. In both cases we get the quantized vortex magnetic fluxes and electric charges.

Chern-Simons vortices and holography

In this paper, based on the $ AdS_{4}/CFT_{3} $ duality, we have explored the precise connection between the abelian Chern-Simons (CS) Higgs model in ($ 2+1 $) dimensions to that with its dual gravitational counterpart living in one higher dimension. It has been observed that the $ U(1) $ current computed at the boundary of the $ AdS_{4} $ could be expressed as the local function of the vortex solution that has the remarkable structural similarity to that with the Ginzburg-Landau (GL) type local expression for the current associated with the Maxwell-CS type vortices in ($ 2+1 $) dimensions. In order to explore this duality a bit further we have also computed the coherence length as well as the magnetic penetration depth associated with these vortices. Finally using the knowledge of both the coherence length as well as the magnetic penetration depth we have computed the Ginzburg-Landau coefficient for the Maxwell-CS type vortices in ($ 2+1 $) dimensions.

GAUGED LIFSHITZ MODEL WITH CHERN–SIMONS TERM

We present a gauged Lifshitz Lagrangian including second- and fourth-order spatial derivatives of the scalar field and a Chern–Simons term, and study nontrivial solutions of the classical equations of motion. While the coefficient β of the fourth-order term should be positive in order to guarantee positivity of the energy, the coefficient α of the quadratic one need not be. We investigate the parameter domains and find significant differences in the field behaviors. Apart from the usual vortex field behavior of the ordinary relativistic Chern–Simons–Higgs model, we find in certain parameter domains oscillatory solutions reminiscent of the modulated phases of Lifshitz systems.

Low-energy vortex dynamics in the self-dual Chern–Simons–Higgs model

The relativistic Chern–Simons–Higgs theory finds application in anyonic superconductivity and contains topological vortices whose dynamics are poorly understood. The gauge fields are defined by a set of nonlinear constraint equations that can be accurately solved with effective Green’s functions, spectral methods, and a discretization scheme using lattice gauge techniques. Simulations show that low-energy two-vortex interactions are elastic with final scattering angles sensitive to vortex velocity; furthermore, vortex pairs form rotating breather states for certain impact parameters. In this study, a function that reproduces scattering angles in the adiabatic limit for nontangential collisions is presented. Simulation results are discussed in the context of analytical methods that extract vortex dynamics from low-energy effective Lagrangians, and a numerical method to calculate the effective Lagrangian is suggested. The numerical techniques used can be applied to the study of other Chern–Simon theories.

Vortex condensation in the dual Chern–Simons–Higgs model

The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern–Simons–Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual Chern–Simons–Higgs model, we determine the location of the critical value for the Chern–Simons parameter below which vortex condensation can happen in the system. The effects of self-energy quantum corrections to the vortex field are also considered.

On the Chern–Simons–Higgs vortex equation without gauge fields

This paper is concerned with the nonself-dual Chern–Simons–Higgs model on R 2 with vanishing gauge fields. We prove the existence of radial solutions with the topological boundary condition, and the nonexistence of radial solutions with the nontopological boundary condition. We also establish the asymptotic properties of solutions and derive the quantization of the potential energy.

Existence of the semilocal Chern–Simons vortices

We consider the Bogomol’nyi equations of the Abelian Chern–Simons–Higgs model with SU(N)global⊗U(1)local symmetry. This is a generalization of the well-known Abelian Chern–Simons–Higgs model with U(1)local symmetry. We prove existence of both topological and nontopological multivortex solutions of the system on the plane.

Nontopological bare solutions in the relativistic self-dual Maxwell–Chern–Simons–Higgs model

In this paper we prove the existence of the radially symmetric nontopological bare solutions in the relativistic self-dual Maxwell–Chern–Simons–Higgs model. We also verify the Chern–Simons limit for those solutions.

Chern–Simons soliton and a critical study of the energy momentum tensor in noncommutative field theory

We have shown unambiguously the existence of solitons in the non-commutative (NC) extension of Chern–Simons–Higgs model. The analysis is done at the classical level (since solitons are essentially classical objects) and in the first non-trivial order in θ, the only spatial noncommutativity parameter. At the same time, we have exposed an inadequacy in the conventional definitions of the energy momentum tensor (EMT) in the present context but this pathology appears to be generic to NC field theories. This is reflected in the fact that the BPS soliton equations (obtained from the EMT) are not compatible with the full variational equations of motion, requiring further imposition a restriction on the form of the Higgs field, contrary to the commutative spacetime case. Both in the Lagrangian and Hamiltonian formulations of the problem, we concentrate on the canonical and symmetric forms of the energy–momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets are derived. In fact the EMT behaves properly as the spacetime translation generators and their actions on the fields are discussed in detail. The effects of noncommutativity on the soliton solutions have been analyzed carefully and we have come up with some interesting results. Comparing the relative strengths of the noncommutative effects, we have shown that there is a universal character in the noncommutative correction to the magnetic field—it depends only on θ. On the other hand, in the cases of all other observables of physical interest, such as the potential profile, soliton mass or the electric field, the parameters θ as well as τ (the latter comprising solely of commutative Chern–Simons–Higgs model parameters) appear with similar weightage.

Uniqueness of the topological multivortex solution in the self-dual Chern–Simons theory

We establish a uniqueness result for the topological multivortex solution to the self-dual equations of the Abelian relativistic self-dual Chern–Simons–Higgs model. We prove that the topological multivortex solution is unique if the Chern–Simons coupling parameter κ>0 is sufficiently small. We also establish a uniqueness result for κ>0 sufficiently large.

Nonself-dual Chern–Simons and Maxwell–Chern–Simons vortices on bounded domains

We first show the existence of the multivortex solutions of Maxwell–Chern–Simons–Higgs (MCSH) model on bounded domains and prove that the solutions of the Euler–Lagrange equations of the MCSH energy functional converge to those of the Abelian–Higgs (AH) model and the Chern–Simons–Higgs (CSH) model in suitable limits, respectively. We also show the existence of the multivortex solutions of the nonself-dual CSH model on bounded domains. Besides, we study asymptotics for the minimizers of MCSH energy functional when the gauge field vanishes.

Radiative corrections to the Chern–Simons term at finite temperature in the noncommutative Chern–Simons–Higgs model

By analyzing the odd parity part of the gauge field two and three point vertex functions, the one-loop radiative correction to the Chern-Simons coefficient is computed in noncommutative Chern-Simons-Higgs model at zero and at high temperature. At high temperature, we show that the static limit of this correction is proportional to $T$ but the first noncommutative correction increases as $T\log T$. Our results are analytic functions of the noncommutative parameter.

New approach to studying the vortex structure of Josephson media equations within the framework of the Chern–Simons–Higgs Lagrangian model

The 2D Josephson type media are supposed to be equivalently modelled by means of Chern–Simons–Higgs geometric Lagrangian functionals. It is shown that the corresponding Chern–Simons–Higgs model possesses of special structure singular geometric objects which can be interpreted as vortices of the Josephson medium. An N-vortex configuration studied in the frame of adiabatic approximation, revealed its particle-like Hamiltonian structure. The two-vortex configuration is investigated in detail, their motion is discussed making use of only analytical tools. Some special solutions are singled out as limiting cases.

Existence of multivortex solutions in the self-dual Chern–Simons–Higgs theory in a background metric

In this paper we show the existence of the multiple multivortex solutions of the self-duality equations of (2+1) dimensional Chern–Simons–Higgs model in a background metric of the form gμν=diag(1,−b(x),−b(x)) with b(x)=O(|x|−l) as |x|→∞ for some l>2.