Generalised point vortices on a plane

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.