Spinning Hopf solitons on S^3 x R

TL;DR

This paper constructs an infinite family of exact spinning Hopf solitons on the space-time S^3 x R, leveraging conformal symmetry and area-preserving diffeomorphisms, revealing bounds on their spin frequencies.

Contribution

It introduces a novel method to generate exact Hopf soliton solutions with spin on S^3 x R using symmetry-based ansatz and topological charge analysis.

Findings

Infinite exact solutions with non-trivial Hopf charge

Spin frequency bounded by inverse of S^3 radius

Utilizes conformal and area-preserving symmetries

Abstract

We consider a field theory with target space being the two dimensional sphere S^2 and defined on the space-time S^3 x R. The Lagrangean is the square of the pull-back of the area form on S^2. It is invariant under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S^2. We construct an infinite number of exact soliton solutions with non-trivial Hopf topological charges. The solutions spin with a frequency which is bounded above by a quantity proportional to the inverse of the radius of S^3. The construction of the solutions is made possible by an ansatz which explores the conformal symmetry and a U(1) subgroup of the area preserving diffeomorphism group.