Chern–Simons vortices in the Gudnason 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.

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.

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.

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.

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.

Vortex condensation in the Chern-Simons Higgs model: An existence theorem

Communications in Mathematical Physics, 1995

It is shown that there is a critical value of the Chern-Simons coupling parameter so that, below the value, there exists self-dual doubly periodic vortex solutions, and, above the value, the vortices are absent. Solutions of such a nature indicate the existence of dyon condensates carrying quantized electric and magnetic charges.

An analysis of the two-vortex case in the Chern-Simons Higgs model

Peking University series in mathematics, 2017

Extending work of Caffarelli-Yang and Tarantello, we present a variational existence proof for two-vortex solutions of the periodic Chern-Simons Higgs model and analyze the asymptotic behavior of these solutions as the parameter coupling the gauge field with the scalar field tends to 0. * dg-ga/9710006

Chern-Simons term and charged vortices in abelian and nonabelian gauge theories

Arxiv preprint hep-th/9505043, 1995

In this article we review some of the recent advances regarding the charged vortex solutions in abelian and nonabelian gauge theories with Chern-Simons (CS) term in two space dimensions. Since these nontrivial results are essentially because of the CS term, hence, we first discuss in some detail the various properties of the CS term in two space dimensions. In particular, it is pointed out that this parity (P) and time reversal (T) violating but gauge invariant term when added to the Maxwell Lagrangian gives a massive gauge quanta and yet the theory is still gauge invariant. Further, the vacuum of such a theory shows the magneto-electric effect. Besides, we show that the CS term can also be generated by spontaneous symmetry breaking as well as by radiative corrections. A detailed discussion about Coleman-Hill theorem is also given which aserts that the parity-odd piece of the vacuum polarization tensor at zero momentum transfer is unaffected by two and multi-loop effects. Topological quantization of the coefficient of the CS term in nonabelian gauge theories is also elaborated in some detail. One of the dramatic effect of the CS term is that the vortices of the abelian (as well as nonabelian) Higgs model now acquire finite quantized charge and angular momentum. The various properties of these vortices are discussed at length with special emphasis on some of the recent developments including the discovery of the self-dual charged vortex solutions.

Vortices in Higgs models with and without Chern-Simons terms

Physics Letters B, 1989

We note that neutrl vortices in a fermionic background acquire the same local charge and spin quantum numbers as charged vortices in a Chern-Simons theory, provided the Chern-Simons mass is obtained by integrating out the fermions. We also point out that in an SU(2) theory involving (globally) charged fermions, (globally) neutral fermions appear as pairs of Z2 solitons and comment on their relevance to condensed matter systems.

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

Journal of Differential Equations, 2015

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 ensuring 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.