The Quantum Hall Fluid and Non-Commutative Chern Simons Theory

By L. Susskind. 2001

329 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7c67cc42ed34888a07dfbf9df87cf59a0ab51c09

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Vanishing of beta function of non-commutative Φ 4 4 theory to all orders (2006, background): “ be important for the future study of more singular models such as Chern-Simons or Yang Mills theories, and in particular for those which have been advocated in connection with the Quantum Hall eﬀect [19, 20, 21]. In this letter we give the complete argument of the vanishing of the beta function at ”
Noncommutative field theory (2001, background): “More recently, it has been proposed that a good description of the fractional quantum Hall effect (FQHE) can be obtained using noncommutative rank 1 ChernSimons theory (Susskind, 2001; Polychronakos, 2001), and we give a brief introduction to these ideas as well.”
Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy (2009, methodology): “8 Earlier models of embedding the FQHE in string theory mainly used the noncommutative Chern-Simons description (as opposed to holographic description) [9, 10, 11, 12, 13, 14, 15].”