One-dimensional topologically nontrivial solutions in the Skyrme model

TL;DR

This paper explores one-dimensional solutions in the Skyrme model, revealing topologically nontrivial configurations due to the fundamental group of SO(3), and introduces a new class of projective models with target spaces RP^d.

Contribution

It explicitly finds and analyzes one-dimensional static solutions in the Skyrme model, including topologically nontrivial finite energy solutions, and proposes a new class of projective models with arbitrary RP^d target spaces.

Findings

Existence of topologically nontrivial solutions in 1D Skyrme model

Explicit solutions with finite energy identified

Introduction of new projective models with RP^d target spaces

Abstract

We consider the Skyrme model using the explicit parameterization of the rotation group SO(3) through elements of its algebra. Topologically nontrivial solutions already arise even in the one-dimensional case because the fundamental group of SO(3) is Z_2. We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy among them. We propose a new class of projective models whose target spaces are arbitrary real projective spaces RP^d.