Abstract
We investigate the existence of self-dual solitons with internal structure in a gauged $O(3)$ nonlinear sigma model immersed in a dielectric medium generated by a real scalar field (dubbed the source field). We consider rotationally symmetric configurations and applying the {Bogomol'nyi-Prasad-Sommerfield} formalism to obtain the energy lower bound and the respective {first-order differential equations (or self-dual equations).} By solving such a system of equations for three different dielectric media, we find the internal structure generates relevant changes in the soliton profiles when compared with the ones obtained without the presence of the dielectric medium.
Highlights
Vortex solutions, in the field theory context, were found in the Maxwell-Higgs model by Nielsen and Olesen, relating them to the Nambu string in the strong-coupling realm [1], besides in the nonrelativistic limit the Abrikosov [2,3] superconducting vortices emerge naturally
An interesting fact about soliton solutions is that in some special situations can be obtained via a system of first-order differential equations attained employing a technique known as the Bogomol’nyi-Prasad-Sommerfield (BPS) formalism, determining the minimum value of the system energy [5,6]
The existence of vortex solutions supporting both electric and magnetic fields have proposed in scenarios involving the ChernSimons action [8,9,10,11,12]
Summary
In the field theory context, were found in the Maxwell-Higgs model by Nielsen and Olesen, relating them to the Nambu string in the strong-coupling realm [1], besides in the nonrelativistic limit the Abrikosov [2,3] superconducting vortices emerge naturally. A first intent, proposed by Schroers, breaks the scale invariance coupling minimally the sigma field to the Maxwell gauge field and introducing a potential that preserves the selfdual structure [20] This way, his approach generated a new class of topological solitons with nonquantized magnetic flux. There are other interesting examples in the literature as the extended groups Uð1Þ × Z2 [29] and CPð2Þ × Z2 [30], being obtained through the introduction of a real scalar field, allowing the description of self-dual vortices in a dielectric medium Such new objects can be of great utility in the study of metamaterials [31,32,33].
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