Abstract
We study time-independent radially symmetric first-order solitons in a CP(2) model interacting with an Abelian gauge field whose dynamics is controlled by the usual Maxwell term. In this sense, we develop a consistent first-order framework verifying the existence of a well-defined lower bound for the corresponding energy. We saturate such a lower bound by focusing on those solutions satisfying a particular set of coupled first-order differential equations. We solve these equations numerically using appropriate boundary conditions giving rise to regular structures possessing finite-energy. We also comment the main features these configurations exhibit. Moreover, we highlight that, despite the different solutions we consider for an auxiliary function β(r) labeling the model (therefore splitting our investigation in two a priori distinct branches), all resulting scenarios engender the very same phenomenology, being physically equivalent.
Highlights
Topological objects are frequently described as the time-independent regular solutions possessing finiteenergy arising from highly nonlinear Euler-Lagrange equations in the presence of appropriated boundary conditions [1]
IV, we present our conclusions and general perspectives regarding future contributions
We end this Section by presenting the numerical solutions we have found for α (r), A (r), B (r) and εbps (r) via the first-order equations (27) and (28) in the presence of the boundary conditions (7) and (31)
Summary
Topological objects are frequently described as the time-independent regular solutions possessing finiteenergy arising from highly nonlinear Euler-Lagrange equations in the presence of appropriated boundary conditions [1]. The Bogomol’nyiPrasad-Sommerfield (BPS) formalism allows to show that these solutions can satisfy a set of coupled firstorder differential equations, the BPS ones [2] In this sense, vortices are radially symmetric solitonic configurations appearing in a planar scalar scenario endowed by a gauge field, their energies being commonly proportional to the magnetic flux, both ones being quantized, i.e. proportional to an integer winding number. We particularize our investigation by focusing on the time-independent fields giving rise to radially symmetric configurations In such a scenario, we look for a consistent first-order framework by manipulating the expression for the effective energy functional in order to establish a well-defined lower bound for the corresponding total energy (here, it is important to point out that such construction is only possible when a particular constraint involving the potential is fulfilled).
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