Nontopological first-order vortices in a gauged $CP(2)$ model with a dielectric function

TL;DR

This paper investigates nontopological first-order solitons in a gauged $CP(2)$ model with a dielectric function, deriving solutions through energy minimization and analyzing their properties and numerical solutions.

Contribution

It introduces a novel first-order framework for nontopological solitons in a gauged $CP(2)$ model with a dielectric function, including explicit solution construction.

Findings

Energy proportional to magnetic flux, both non-quantized

Derived explicit dielectric function and potential for solutions

Numerical solutions illustrating soliton properties

Abstract

We consider nontopological first-order solitons arising from a gauged $CP(2)$ model in the presence of the Maxwell term multiplied by a nontrivial dielectric function. We implement the corresponding first-order scenario by proceeding the minimization of the total energy, this way introducing the corresponding energy lower-bound, such a construction being only possible due to a differential constraint including the dielectric function itself and the self-interacting potential defining the model. We saturate the aforementioned bound by focusing our attention on those solutions fulfilling a particular set of two coupled first-order differential equations. In the sequel, in order to solve these equations, we choose the dielectric function explicitly, also calculating the corresponding self-interacting potential. We impose appropriate boundary conditions supporting nontopological solitons, from which we verify that the energy of final structures is proportional to the magnetic flux they engender, both quantities being not quantized, as expected. We depict the new numerical solutions, whilst commenting on the main properties they present.