Topological vortices in generalized Born–Infeld–Higgs electrodynamics

Casana, R.; Hora, E. da; Rubiera-García, Diego; Santos, Caroline

doi:10.1140/epjc/s10052-015-3596-1

Cited by 23 publications

(34 citation statements)

References 66 publications

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“…[31]. Thenceforth, several papers have addressed this issue in various contexts [32][33][34][35][36][37][38][39][40][41][42]. However, as far as we know, the first paper that studied this issue is from 1991 in Ref.…”

Section: Introductionmentioning

confidence: 99%

First order formalism for generalized vortices

et al. 2018

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This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the construction of models that support vortices that obey the stressless condition and lead to first order differential equations which are compatible with the equations of motion. The results induce the appearance of constraints that restrict the choice of the Lagrangian densities, but help us to introduce an auxiliary function that allows to calculate the energy without knowing the explicit form of the solutions. * Electronic address: bazeia@fisica.ufpb.br † Electronic address:In the current work, we concentrate on vortices in relativistic models described in (2, 1) spacetime dimensions. As it is known, vortices were firstly studied by Helmholtz in Ref. [4] and are commonly found in fluid mechanics [5]. They are also present in condensed matter when one studies superconductors. As it is well-known, when superconductors are below a critical temperature they expel the magnetic field, a phenomenom known as the Meissner effect [6]. However, working with the Ginzburg-Landau theory of superconductivity [7], in Ref.[8] Abrikosov noticed that vortices also appear in type II superconductors when exposed to an external electromagnetic field in a specific range of values.The Ginzburg-Landau theory is nonrelativistic. Nevertheless, it is possible to find relativistic field theories that support vortex solutions. The first model was proposed by Nielsen and Olesen in Ref. [9]; it consists of a complex scalar field minimally coupled with a Maxwell gauge field under under the action of the local U (1) gauge symmetry. The equations of the fields that describe the problem, however, are of second order involving the two aforementioned fields that interact in a nontrivial way. Even so, by setting an additional condition to the stress tensor, a classical solution was found in Ref.[10] by de Vega and Schaposnik.Moreover, in Ref.[11] Bogomol'nyi found first order differential equations compatible with the equations of motion by minimizing the energy of the field configurations. The procedure developed by Bogomol'nyi works for kinks, vortices and monopoles, and joined the work of Prasad and Sommerfield [12] on monopoles, to make what is now called BPS states, which represent solutions of first order differential equations that solve the equations of motion and minimize the energy of the non-trivial static field configurations that describe the topological structures.

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Section: Introductionmentioning

confidence: 99%

First order formalism for generalized vortices

et al. 2018

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“…One generalization of BIH model was firstly done in [52] but no self-dual solutions were found. On the other hand, the self-dual or BPS topological vortex solutions were found in a generalized Born-Infeld-Higgs model introduced in [62]. The Lagrangian density of our (2+1)-dimensional theory is written as…”

Section: The Born-infeld-higgs Casementioning

confidence: 99%

Self-Dual Effective Compact and True Compacton Configurations in Generalized Abelian Higgs Models

Casana

Lazar

Sourrouille

2018

Advances in High Energy Physics

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We have studied the existence of self-dual effective compact and true compacton configurations in Abelian Higgs models with generalized dynamics. We have named an effective compact solution the one whose profile behavior is very similar to the one of a compacton structure but still preserves a tail in its asymptotic decay. In particular, we have investigated the electrically neutral configurations of the Maxwell-Higgs and Born-Infeld-Higgs models and the electrically charged ones of the Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs models. The generalization of the kinetic terms is performed by means of dielectric functions in gauge and Higgs sectors. The implementation of the BPS formalism without the need to use a specific Ansatz has led us to the explicit determination for the dielectric function associated with the Higgs sector to be proportional to | | 2 −2 , > 1. Consequently, the followed procedure allows us to determine explicitly new families of self-dual potential for every model. We have also observed that, for sufficiently large values of , every model supports effective compact vortices. The true compacton solutions arising for = ∞ are analytical. Therefore, these new self-dual structures enhance the space of BPS solutions of the Abelian Higgs models and they probably will imply interesting applications in physics and mathematics.

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“…Among them we can cite the problem of the localization of gravity and/or particle/field in a 6-D braneworld [41] and the Born-Infeld-Higgs models [42,43]. Another interesting scenario for to study Maxwell-Higgs models is related to cosmic strings, topological defects similar to the vortices, which may have great importance in the evolution of the Cosmos and formation of the structures existing in the Universe [44][45][46][47][48].…”

Section: Jhep12(2016)051mentioning

confidence: 99%

“…In the Higgs sector, w(|φ|) must be positive, whilst V (|φ|) represents some convenient potential. The Lagrangian density (2.1) allows to describe many of the generalized models present in the literature, for example, we can recover Born-Infeld-Higgs ones [42,43], the prototype of highly nonlinear gauge field dynamics.…”

Section: Jhep12(2016)051mentioning

confidence: 99%

Self-dual configurations in Abelian Higgs models with k-generalized gauge field dynamics

Casana

Cavalcante

Hora

2016

J. High Energ. Phys.

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Abstract:We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a k-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of F µν F µν . We have implemented our proposal by means of a k-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol'nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of k-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or ChernSimons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with |φ| 4 -potential or |φ| 6 -potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the k-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.

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Topological vortices in generalized Born–Infeld–Higgs electrodynamics

Cited by 23 publications

References 66 publications

First order formalism for generalized vortices

First order formalism for generalized vortices

Self-Dual Effective Compact and True Compacton Configurations in Generalized Abelian Higgs Models

Self-dual configurations in Abelian Higgs models with k-generalized gauge field dynamics

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