Abstract
We have shown the existence of self-dual solitons in a type of generalized Chern-Simons baby Skyrme model where the generalized function (depending only in the Skyrme field) is coupled to the sigma-model term. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism requires the generalizing function becomes the superpotential defining properly the self-dual potential. Thus, we have obtained a topological energy lower-bound (Bogomol'nyi bound) and the self-dual equations satisfied by the fields saturating such a bound. The Bogomol'nyi bound being proportional to the topological charge of the Skyrme field is quantized whereas the total magnetic flux is not. Such as expected in a Chern-Simons model the total magnetic flux and the total electrical charge are proportional to each other. Thus, by considering the superpotential a well-behaved function in the whole target space we have shown the existence of three types of self-dual solutions: compacton solitons, soliton solutions whose tail decays following an exponential-law $e^{-\alpha r^{2}}$ ($\alpha>0$), and solitons having a power-law decay $r^{-\beta}$ ($\beta>0$). The profiles of the two last solitons can exhibit a compactonlike behavior. The self-dual equations have been solved numerically and we have depicted the soliton profiles, commenting on the main characteristics exhibited by them.
Highlights
Effective field theories have an important role in physics, especially when they can provide answers or insights about certain physical properties that could be difficult or even impossible to extracted from the respective underlying higher-energy model
The implementation of the BPS formalism looks successful; there is a contradiction with the hypothesis about the functional dependence of the potential shown in the Lagrangian density (3)
Our analysis of the compacton solitons has allowed us to conclude that the gauge vacuum value aR only depends on the electromagnetic coupling constant g; the total magnetic flux is independent from the values of κ and λ, and it becomes quantized for sufficiently large values of g
Summary
Effective field theories have an important role in physics, especially when they can provide answers or insights about certain physical properties that could be difficult or even impossible to extracted from the respective underlying higher-energy model. A Skyrmion crystal with a triangular array in magnetic systems was shown to have strong similarities with the Abrikosov vortex lattice in type-II superconductors [21] All these planar realizations and residual problems in the Skyrme approach on nuclear physics has inspired the development of a lower-dimensional version of the Skyrme model called the baby Skyrme model [22,23]. The goal of the manuscript is the successful implementation of the BPS formalism in a generalized version of a gauged baby Skyrme model in which the gauge field dynamics is governed solely by the Chern-Simons term Such a model is able to engender BPS compacton and noncompacton solitons, and the latter ones can exhibit compactonlike behavior.
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