Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions

TL;DR

This paper constructs higher-dimensional Lorentz invariant field theories with integrability and conformal symmetry, enabling exact solutions with non-trivial Hopf charges, advancing understanding of topological solitons.

Contribution

It introduces a class of integrable, conformally symmetric models with exact Hopfion solutions in higher dimensions, linking integrability, symmetry, and topological charges.

Findings

Models possess infinite local conserved currents.

Existence of an ansatz for solutions with Hopf charges.

Models exhibit conformal symmetry and stability of static solutions.

Abstract

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target space. Requiring the existence of Lagrangean and the stability of static solutions singles out a class of models which have an additional conformal symmetry. That is used to explain the existence of an ansatz leading to solutions with non trivial Hopf charges.