A Quantum Hall Fluid of Vortices

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.

10 pages. v2(3): (More) References added

References in corpus (1)

• Vortices, Instantons and Branes

Cited by in corpus (12)

• Non-Abelian 3d Bosonization and Quantum Hall States
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories
• A Matrix Model for Non-Abelian Quantum Hall States
• A Matrix Model for WZW
• Slow Schroedinger dynamics of gauged vortices
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model
• ADHM and the 4d Quantum Hall Effect
• Matrix supergroup Chern-Simons models for vortex-antivortex systems
• Vortex counting and the quantum Hall effect
• Roton-phonon excitations in Chern-Simons matter theory at finite density