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

Abstract

We study a 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, \(\omega_1(|\phi|)\) and \(\omega(|\phi|)\), which split the kinetic term - \(|D_\mu\phi|^2 \rightarrow \omega_1 (|\phi|) |D_0\phi|^2-\omega(|\phi|) |D_k\phi|^2\) - of the Higgs field and break explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether \(\omega \propto \beta |\phi|^{2\beta-2}\) with \(\beta\geq 1\). The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function \(\omega_1(|\phi|)\) which must be able to provide a finite magnetic field. Among them we have selected the simplest ones which in some particular limits reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual \(|\phi|^6\)-vortex solutions have been analyzed both from theoretical and numerical point of view.