A Quantum Hall Fluid of Vortices

TL;DR

This paper demonstrates that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid, connecting vortex dynamics with matrix mechanics and non-commutative hydrodynamics, supported by D-brane realizations.

Contribution

It establishes a novel link between vortex dynamics in Chern-Simons theory and quantum Hall physics, integrating matrix mechanics and non-commutative geometry.

Findings

Vortices form a quantum Hall fluid.

Vortex dynamics follow Polychronakos' matrix mechanics.

Large vortex number leads to non-commutative hydrodynamics.

Abstract

In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of the quantum Hall droplet. As the number of vortices becomes large, they fill the plane and a hydrodynamic treatment becomes possible, resulting in the non-commutative theory of Susskind. Key to the story is the recent D-brane realisation of vortices and their moduli spaces.