Self-Dual Configurations in a Generalized Abelian Chern-Simons-Higgs Model with Explicit Breaking of the Lorentz Covariance (original) (raw)

Self-dual Maxwell–Chern–Simons solitons from a Lorentz-violating model

Physics Letters B, 2013

Self-dual abelian Higgs system, involving both the Maxwell and Chern-Simons terms are obtained from Carroll-Field-Jackiw theory by dimensional reduction. Bogomol'nyi-type equations are studied from theoretical and numerical point of view. In particular we show that the solutions of these equations are Nielsen-Olesen vortices with electric charge.

Vortices in generalized Abelian Chern-Simons-Higgs model

arXiv: High Energy Physics - Theory, 2015

We study a generalization of abelian Chern-Simons-Higgs model by introducing nonstandard kinetic terms. We will obtain a generic form of Bogomolnyi equations by minimizing the energy functional of the model. This generic form of Bogomolnyi equations produce an infinity number of soliton solutions. As a particular limit of these generic Bogomolnyi equations, we obtain the Bogomolnyi equations of the abelian Maxwell-Higgs model and the abelian Chern-Simons Higgs model. Finally, novel soliton solutions emerge from these generic Bogomolnyi equations. We analyze these solutions from theoretical and numerical point of view.

Electric-dual BPS Vortices in The Generalized Self-dual Maxwell-Chern-Simons-Higgs Model

arXiv (Cornell University), 2021

In this paper we show how to derive the Bogomolny's equations of the generalized self-dual Maxwell-Chern-Simons-Higgs model presented in [1] by using the BPS Lagrangian method with a particular choice of the BPS Lagrangian density. We also show that the identification, potential terms, and Gauss's law constraint can be derived rigorously under the BPS Lagrangian method. 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 = ±A 0 , which is different by a relative sign to the identification in [1], N = ∓A 0. Under this identification, N = ±A 0 , we obtain a slightly different potential terms and Bogomolny's equations compared to the ones in [1]. Furthermore we compute the solutions numerically, with the same configurations as in [1], and find that only the resulting electric field plots differ by sign relative to the results in [1]. Therefore we conclude that these BPS vortices are electric-dual BPS vortices of the ones computed in [1].

A generalized self-dual Chern-Simons Higgs theory

Letters in Mathematical Physics, 1991

In the recently discovered Chern-Slmons model, the reduction to a Bogomol'nyi bound or self-duality depends crucially on the specific form of the Higgs potential energy function, which is characterized by a ~b 6 type self-interaction. The purpose of this paper is to show that a much wider class of Higgs self-interaction may be allowed to achieve self-duality provided that the kinetic energy term of the Higgs scalar is suitably modified. The existence of topological multivortex solutions is also established. Furthermore, it 1s remarked that the Melssner effect may occur in the model.

Generalized self-duality for the Yang-Mills-Higgs system

Physical Review D, 2021

Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative methods. We present a generalization of the Yang-Mills-Higgs system by the introduction of scalar fields assembled in a symmetric and invertible matrix h of the same dimension as the gauge group. The coupling of such new fields to the gauge and Higgs fields is made by replacing the Killing form, in the contraction of the group indices, by the matrix h in the kinetic term for the gauge fields, and by its inverse in the Higgs field kinetic term. The theory is conformally invariant in the three dimensional space IR 3. An important aspect of the model is that for practically all configurations of the gauge and Higgs fields the new scalar fields adjust themselves to solve the modified self-duality equations. We construct solutions using a spherically symmetric ansätz and show that the 't Hooft-Polyakov monopole becomes a self-dual solution of such modified Yang-Mills-Higgs system. We use an ansätz based on the conformal symmetry to construct vacuum solutions presenting non-trivial toroidal magnetic fields.

Resolution of Chern–Simons–Higgs Vortex Equations

Communications in Mathematical Physics, 2016

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern-Simons-Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix K of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.

Generalized self-dual Maxwell-Chern-Simons-Higgs model

Physical Review D, 2012

We present a consistent BPS framework for a generalized Maxwell-Chern-Simons-Higgs model. The overall model, including its self-dual potential, depends on three different functions, h (|φ| , N ), w (|φ|) and G (|φ|), which are functions of the scalar fields only. The BPS energy is proportional to the magnetic flux when w (|φ|) and G (|φ|) are related to each other by a differential constraint. We present an explicit non-standard model and its topologically non-trivial static configurations, which are described by the usual radially symmetric profile. Finally, we note that the non-standard results behave in a similar way as their standard counterparts, as expected, reinforcing the consistence of the overall construction.

On the solitons of the Chern-Simons-Higgs model

The European Physical Journal C, 1999

Several issues concerning the self-dual solutions of the Chern-Simons-Higgs model are addressed. The topology of the configuration space of the model is analysed when the space manifold is either the plane or an infinite cylinder. We study the local structure of the moduli space of self-dual solitons in the second case by means of an index computation. It is shown how to manage the non-integer contribution to the heat-kernel supertrace due to the non-compactness of the base space. A physical picture of the local coordinates parametrizing the non-topological soliton moduli space arises .

Peculiar charged vortices in Higgs models with pure Chern-Simons term

Physics Letters B, 1990

We show that abelian as well as nonabelian Higgs models in (2+ 1) dimensions with the pure Chern-Simons term possess peculiar charged vortex solutions of finite energy. For all of them the magnetic field vanishes not only at infinity but also at the origin. Such objects can also be shown to exist in an abelian Higgs model without the Chern-Simons term but with non-minimal coupling.