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The Quantum Hall Fluid and Non-Commutative Chern Simons Theory

L. Susskind
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Abstract

The first part of this paper is a review of the author's work with S. Bahcall which gave an elementary derivation of the Chern Simons description of the Quantum Hall effect for filling fraction $1/n$. The notation has been modernized to conform with standard gauge theory conventions. In the second part arguments are given to support the claim that abelian non-commutative Chern Simons theory at level $n$ is exactly equivalent to the Laughlin theory at filling fraction $1/n$. The theory may also be formulated as a matrix theory similar to that describing D0-branes in string theory. Finally it can also be thought of as the quantum theory of mappings between two non-commutative spaces, the first being the target space and the second being the base space.

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L. Susskind. 2001-01-14. The Quantum Hall Fluid and Non-Commutative Chern Simons Theory. https://arxiv.org/abs/hep-th/0101029

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