Hierarchy Construction of Quantum Hall States and Non-Commutative Chern-Simons Theory

TL;DR

This paper develops a non-commutative Chern-Simons framework for constructing the hierarchy of quantum Hall states, extending Susskind's approach to generic filling fractions and connecting it with existing effective field theories.

Contribution

It introduces a method to realize the hierarchy of quantum Hall states with arbitrary filling fractions using non-commutative Chern-Simons theory based on area-preserving diffeomorphisms.

Findings

Hierarchy construction via non-commutative Chern-Simons theory

Extension of Susskind's approach to generic filling fractions

Discussion of relation to previous effective field theories

Abstract

In this paper, we study the non-commutative Chern-Simons description of the hierarchy of quantum Hall states. Our method is based on the framework suggested by Susskind in hep-th/0101029. By using the area preserving diffeomorphism gauge symmetry of quasiparticle fluid, we show that non-commutative Chern-Simons description of the hierarchy construction of quantum Hall states with generic filling fraction can be realized in Susskind's approach. The relationship between our model and the pervious work on the effective field theory of quantum Hall states is also discussed.