Approximate vortex solution of Faddeev model

TL;DR

This paper derives an approximate analytic vortex solution for the Faddeev model by transforming the static field equations into an algebraic ODE, aiming to minimize vortex energy and analyze its dependence on topological charge.

Contribution

It introduces a novel Ansatz that simplifies the Faddeev model's equations into an algebraic ODE, providing an approximate solution that minimizes vortex energy.

Findings

Vortex energy is approximately proportional to the topological charge.

An approximate analytic expression for the vortex solution is obtained.

The method simplifies the analysis of vortex solutions in the Faddeev model.

Abstract

Through an Ansatz specifying the azimuthal-angle dependence of the solution, the static field equation for vortex of the Faddeev model is converted to an algebraic ordinary differential equation. An approximate analytic expression of the vortex solution is explored so that the energy per unit vortex length becomes as small as possible. It is observed that the minimum energy of vortex is approximately proportional to the integer which specifies the solution.