A Class of Exact Solutions of the Faddeev Model

TL;DR

This paper derives a class of exact solutions for the Faddeev model, a nonlinear sigma model with Skyrme term, interprets them geometrically, and explores a specific static vortex solution numerically, linking it to the Skyrme model.

Contribution

It presents a new class of exact solutions for the Faddeev model and establishes its equivalence to the mesonic sector of the SU(2) Skyrme model.

Findings

Exact solutions interpreted as isothermal coordinates.

Numerical analysis of a static vortex solution.

Faddeev model's equivalence to the SU(2) Skyrme model's mesonic sector.

Abstract

A class of exact solutions of the Faddeev model, that is, the modified SO(3) nonlinear sigma model with the Skyrme term, is obtained in the four dimensional Minkowskian spacetime. The solutions are interpreted as the isothermal coordinates of a Riemannian surface. One special solution of the static vortex type is investigated numerically. It is also shown that the Faddeev model is equivalent to the mesonic sector of the SU(2) Skyrme model where the baryon number current vanishes.