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

Abstract EN

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, ω 1 ( | ϕ | ) and ω ( | ϕ | ) , which split the kinetic term of the Higgs field, | D μ ϕ | 2 → ω 1 ( | ϕ | ) | D 0 ϕ | 2 - ω ( | ϕ | ) | D k ϕ | 2 , breaking explicitly the Lorentz covariance.

We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether ω ( | ϕ | ) ∝ β | ϕ | 2 β - 2 with β ≥ 1 .

The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ω 1 ( | 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.