A Geometric Algorithm to construct new solitons in the O(3) Nonlinear Sigma Model

TL;DR

This paper introduces a geometric algorithm for constructing symmetric soliton solutions in the O(3) nonlinear sigma model, linking boundary conditions to topological charges and generating new solutions in the free model.

Contribution

It presents a novel geometric method to find all symmetric solitons in the boundary-bound O(3) sigma model, reducing the problem to elastica in hyperbolic space.

Findings

Algorithm determines all boundary-preserving solitons.

Solutions relate boundary conditions to topological charges.

New soliton solutions are derived for the free model.

Abstract

The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a limiting case, we give a wide family of new soliton solutions in the free O(3) nonlinear sigma model.