# Topological first-order vortices in a gauged CP(2) model

## TL;DR

This paper investigates radially symmetric first-order solitons in a gauged CP(2) model with Maxwell dynamics, establishing a lower energy bound, solving the equations numerically, and analyzing the physical equivalence of different solution branches.

## Contribution

It develops a first-order framework for gauged CP(2) solitons, demonstrating the existence of finite-energy solutions and showing different auxiliary function choices lead to equivalent physical phenomena.

## Key findings

- Existence of a well-defined energy lower bound.
- Numerical solutions for regular finite-energy configurations.
- Different solution branches are physically equivalent.

## 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 $\beta \left( r\right) $ labeling the model (therefore splitting our investigation in two a priori distinct branches), all resulting scenarios engender the very same phenomenology, being physically equivalent.