Semilocal string with Lorentz-breaking term

Full text: Topological defects arising from the spontaneous symmetry breaking are physical systems of interest in a wide range of theories, from condensed matter to cosmology. These defects may arise from an abelian, as well as non-abelian, symmetry spontaneously broken. The type of the defect depends on the broken symmetry. Among the typical interesting defects are the vortex solutions, whose characteristics were extensively investigated in the literature. On the other hand,extensions of the standard model including Lorentz-violation terms have been greatly studied in recent years. It was demonstrated that a Maxwell-Higgs systems with a CPT-even Lorentz symmetry violating term yields Bogomolnyi-Prasad-Sommerfield (BPS) vortex solutions enjoying fractional quantization of the magnetic field. One of the benchmarks of the vortex theory is the semi local vortex. Usually, most part of the study of vortex was restricted to the local symmetry. However, the inclusion of a global symmetry, besides the usual local one, may lead to some interesting characteristics in the resulting topological defect as the presence of topological vortex even if the vacuum manifold is simply connected. This work is partially concerned with the demonstration that semi local vortices may be found in a usual Maxwell-Higgs system plus a CPT-even Lorentz symmetry violating term. In fact, starting from a SU(2) global x U(1) local symmetry, the symmetry breaks down to U(1) local. Hence, the first homotopy group is trivial, i. e., π₁(SU(2)globalxU(1)local=U(1)local) = 1. However, the local symmetry also plays its role. Since the potential we shall deal with goes as usual, it is possible to say that as in the usual Higgs-Maxwell case , when no Lorentz-violating term is present, the arguments in favor of stable vortices are strong, but not exhaustive. In order to guarantee the existence of semi local vortices in the Maxwell-Higgs plus Lorentz-violating model, we have to construct the solutions. It was shown that the presence of the Lorentz symmetry violating term may lead to a peculiar effect in the vortex size. Hence,in view of the aforementioned characteristic of the semi local vortex, the solution combining both effects may result in a most malleable defect structure, which is shown to be the case. Besides, we show that the Bradlows limit depends on the magnitude of a parameter related to the Lorentz-breaking term, i. e., the vorticity is also affected. In fact, the vorticity increases as the Lorentz violating term becomes more relevant. (author)