From Hopf fibrations to exotic causal replacements

TL;DR

This paper explores wave propagation around a static Hopf soliton in the Nicole model, revealing nonlinear lensing effects in the geometrical optics limit, with implications for topological field theories like the Skyrme model.

Contribution

It demonstrates the emergence of nonlinear lensing effects near Hopf solitons within the Nicole model, highlighting potential phenomena in related topological field theories.

Findings

Nontrivial lensing effects due to nonlinear interactions.

Effects occur when the theory remains hyperbolic.

Implications for effective field theories with topological invariants.

Abstract

Topological solitons are relevant in several areas of physics [1]. Recently, these configurations have been investigated in contexts as diverse as hydrodynamics [2], Bose-Einstein condensates [3], ferromagnetism [4], knotted light [5] and non-abelian gauge theories [6]. In this paper we address the issue of wave propagation about a static Hopf soliton in the context of the Nicole model. Working within the geometrical optics limit we show that several nontrivial lensing effects emerge due to nonlinear interactions as long as the theory remains hyperbolic. We conclude that similar effects are very likely to occur in effective field theories characterized by a topological invariant such as the Skyrme model of pions.