Finite Noncommutative Chern-Simons with a Wilson Line and the Quantum Hall Effect

TL;DR

This paper introduces a finite matrix model for noncommutative Chern-Simons theory with Wilson lines, connecting it to quantum Hall fluids and their multilayered variants.

Contribution

It develops a finite-dimensional matrix model incorporating Wilson lines, extending previous models to describe multilayer quantum Hall systems.

Findings

Finite matrix model compatible with quantum Hall droplets.

Generalizations to multilayered quantum Hall fluids.

Connections between noncommutative Chern-Simons theory and quantum Hall effects.

Abstract

We present a finite dimensional matrix model associated to the noncommutative Chern-Simons theory, obtained by inserting a Wilson line. For a specific choice of the representation of the Wilson line the model is equivalent to the minimal modification of the matrix model which is compatible with finite dimensional matrices, and was introduced previously to study droplets of quantum Hall fluid. For other representations we obtain generalizations corresponding to regularized U(n) Chern-Simons theoris, representing multilayered quantum Hall fluids.