Exact time dependent Hopf solitons in 3+1 dimensions

TL;DR

This paper constructs an infinite family of exact, time-dependent Hopf soliton solutions in a 3+1 dimensional Lorentz invariant model with target space S^2, revealing integrability and potential relevance to gauge theories.

Contribution

It introduces a novel method to generate exact, time-dependent Hopf solitons in four dimensions using conformal and area-preserving symmetries, demonstrating integrability.

Findings

Infinite exact solutions with Hopf charge

Model exhibits integrability in 4D

Potential implications for gauge theory low-energy limits

Abstract

We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S^2. The construction is based on an ansatz which explores the invariance of the model under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S^2. The model is a rare example of an integrable theory in four dimensions, and the solitons may play a role in the low energy limit of gauge theories.