Stationary ring solitons in field theory - knots and vortons

TL;DR

This paper reviews stationary vortex ring solutions in classical field theories, including static knots, spinning solitons, and vortons, highlighting their properties, stability, and analogs in condensed matter systems.

Contribution

It provides the first explicit construction of global vortons as non-radiating solutions and discusses various stationary and spinning vortex ring solutions across different field theories.

Findings

Explicit construction of global vortons demonstrating non-radiating behavior

Identification of stationary knot solitons stabilized by topological charges

Descriptions of spinning and gauged vortex solutions in various field theories

Abstract

We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning $Q$-balls, their twisted and gauged generalizations reported here for the first time, spinning skyrmions, and rotating monopole-antimonopole pairs. We then present the first explicit construction of global vortons as solutions of the elliptic boundary value problem, which demonstrates their non-radiating character. Finally, we describe the analogs of vortons in the Bose-Einstein condensates, analogs of spinning $Q$-balls in the non-linear optics, and also moving vortex rings in superfluid helium and in ferromagnetics.