Edge excitations of the Chern Simons matrix theory for the FQHE

TL;DR

This paper analyzes the edge excitations in the Chern-Simons matrix theory for fractional quantum Hall states, deriving an effective boundary theory equivalent to a chiral boson model.

Contribution

It provides a semiclassical analysis linking bulk and edge degrees of freedom, establishing the boundary theory as a chiral boson on the circle.

Findings

Identified bulk and edge degrees of freedom in the Chern-Simons matrix theory.

Derived an effective boundary theory matching the chiral boson model.

Showed the boundary excitations correspond to a chiral boson on the circle.

Abstract

We study the edge excitations of the Chern Simons matrix theory, describing the Laughlin fluids for filling fraction $\nu=\frac{1}{k}$, with $k$ an integer. Based on the semiclassical solutions of the theory, we are able to identify the bulk and edge degrees of freedom. In this way we can freeze the bulk of the theory, to the semiclassical values, obtaining an effective theory governing the boundary excitations of the Chern Simons matrix theory. Finally, we show that this effective theory is equal to the chiral boson theory on the circle.