Self-dual configurations in a generalized Abelian Chern-Simons-Higgs model with explicit breaking of the Lorentz covariance

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 - $|D_μϕ|^2 \rightarrowω_1 (|ϕ|)|D_0ϕ|^2-ω(|ϕ|) |D_kϕ|^2$ - breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether $ω(|ϕ|) \propto β|ϕ|^{2β-2}$ with $β\geq 1$. 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 both from theoretical and numerical point of view.

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