Faddeev-Skyrme Model and Rational Maps

TL;DR

This paper explores the Faddeev-Skyrme model, reformulating it into a Skyrme-like gauge-equivalent form, and analyzes solitonic solutions using rational maps, establishing energy bounds and extending to SU(N) theories.

Contribution

It introduces a gauge-equivalent reformulation of the Faddeev-Skyrme model and applies the rational map ansatz to analyze solitons, also extending the model to SU(N) Yang-Mills theories.

Findings

Established energy function and Bogomolny bound for solitons.

Reformulated the model into a Skyrme-like gauge form.

Extended the model to infrared limits of SU(N) Yang-Mills.

Abstract

The Faddeev-Skyrme model, a modified O(3) nonlinear sigma model in three space dimensions, is known to admit topological solitons that are stabilized by the Hopf charge. The Faddeev-Skyrme model is also related to the low-energy limits of SU(2) Yang-Mills theory. Here, the model is reformulated into its gauge-equivalent expression, which turns out to be Skyrme-like. The solitonic solutions of this Skyrme-like model are analyzed by the rational map ansatz. The energy function and the Bogomolny-type lower bound of the energy are established. The generalized Faddeev-Skyrme model that originates from the infrared limits of SU(N) Yang-Mills theory is presented.