Generalised point vortices on a plane

TL;DR

This paper introduces integrable generalisations of the three-vortex system on a plane using Lie algebra root vectors, extending the model with spin degrees of freedom and highlighting its scale invariance for potential holographic applications.

Contribution

It proposes new integrable vortex models based on Lie algebra structures and extends them with spin, broadening the understanding of vortex dynamics and symmetries.

Findings

Generalised vortex systems are integrable and governed by positive definite Hamiltonians.

Extended models include spin degrees of freedom, maintaining integrability.

The models exhibit nonrelativistic scale invariance, relevant for holography.

Abstract

A three-vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three-vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that a generalised system, which is governed by a positive definite Hamiltonian, admits a natural integrable extension by spin degrees of freedom. It is emphasised that the n-vortex planar model and plenty of its generalisations enjoy the nonrelativistic scale invariance, which gives room for possible holographic applications.