On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory

TL;DR

This paper explores noncommutative Maxwell-Chern-Simons theory, revealing new plane wave and vortex solutions that could model Quantum Hall transitions, with findings on their spectrum, polarization, and asymptotic behavior.

Contribution

It introduces and analyzes novel noncommutative plane wave and vortex solutions, expanding understanding of gauge theories relevant to Quantum Hall physics.

Findings

Identified a series of noncommutative massive plane wave solutions.

Derived a nonlinear difference equation for vortex solutions.

Found asymptotic forms of vortex solutions.

Abstract

We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive ``plane wave'' solutions with polarization dependent on the magnitude of the wave-vector. The mass of each branch is fixed by the quantization condition imposed on the coefficient of the noncommutative Chern-Simons term. For the radially symmetric ansatz a vortex-like solution is found and investigated. We derive a nonlinear difference equation describing these solutions and we find their asymptotic form. These excitations should be relevant in describing the Quantum Hall transitions between plateaus and the end transition to the Hall Insulator.