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

Rodolfo Casana,Lucas Sourrouille

doi:10.1155/2016/5315649

Abstract

We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions,ω1(|ϕ|)andω(|ϕ|), which split the kinetic term of the Higgs field,|Dμϕ|2→ω1(|ϕ|)|D0ϕ|2-ω(|ϕ|)|Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whetherω(|ϕ|)∝β|ϕ|2β-2withβ≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing functionω1(|ϕ|)which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual|ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.

Highlights

A time ago it was shown that (1+2)-dimensional matter field interacting with gauge fields whose dynamics is governed by a Chern-Simons term supports soliton solutions [1, 2]
The ChernSimons gauge field dynamic remains the same when coupled with matter fields either relativistic [8, 9] or nonrelativistic [10, 11]
The investigations concerning the topological structure of the k-field theories have shown that they support topological soliton solutions both in pure matter models and in gauged field models [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]

Summary

Introduction

A time ago it was shown that (1+2)-dimensional matter field interacting with gauge fields whose dynamics is governed by a Chern-Simons term supports soliton solutions [1, 2] (for a review see [3,4,5,6,7]). These models have the particularity to become self-dual when the self-interactions are suitably chosen [8,9,10,11]. We have constructed, analytically and numerically, novel soliton solutions for some values of N and M

The Theoretical Framework

Some Simple Models

Remarks and Conclusions