First-order vortices in a gauged $CP(2)$ model with a Chern-Simons term

TL;DR

This paper explores radially symmetric, topologically nontrivial solutions in a gauged $CP(2)$ model with a Chern-Simons term, developing a first-order framework and numerically solving for energy-minimizing configurations.

Contribution

It introduces a first-order Bogomol'nyi framework for the gauged $CP(2)$ model with Chern-Simons term, enabling the construction of topological vortex solutions.

Findings

Derived energy lower-bound and first-order equations.

Numerically obtained vortex profiles with topological properties.

Analyzed properties of the solutions and their physical implications.

Abstract

We consider a gauged $CP(2)$ theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the Bogomol'nyi prescription, from which we obtain the corresponding energy lower-bound and the first-order equations the model supports. We use these expressions to introduce effective BPS scenarios, solving the resulting first-order equations by means of the finite-difference scheme, this way attaining genuine field solutions engendering topological configurations. We depict the new profiles, commenting on the main properties they engender.