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

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, ${\omega }_1(|\varphi |)$ and $\omega (|\varphi |)$, which split the kinetic term of the Higgs field - $|D_{\mu }\varphi {|}^2\to {\omega }_1(|\varphi |)|D_0\varphi {|}^2-\omega (|\varphi |)|D_k\varphi {|}^2$ - breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether $\omega (|\varphi |)\propto \beta |\varphi {|}^{2\beta -2}$ with $\beta \ge 1$. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ${\omega }_1(|\varphi |)$ 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 $|\varphi {|}^6$-vortex solutions have been analyzed both from theoretical and numerical point of view.

7 Latex 2e pages, 5 .eps figures

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Cited by in corpus (1)

• Self-dual effective compact and true compacton configurations in generalized Abelian Higgs models