Noncommutative Chern-Simons terms and the noncommutative vacuum

It is pointed out that the space noncommutativity parameters $theta^{\mu \nu}$ in noncommutative gauge theory can be considered as a set of superselection parameters, in analogy with the theta-angle in ordinary gauge theories. As such, they do not need to enter explicitly into the action. A simple generic formula is then suggested to reproduce the Chern-Simons action in noncommutative gauge theory, which reduces to the standard action in the commutative limit but in general implies a cascade of lower-dimensional Chern-Simons terms. The presence of these terms in general alters the vacuum structure of the theory and nonstandard gauge theories can emerge around the new vacua.Comment: 10 pages, no figures; minor typos and references correcte

Quantum Hall states as matrix Chern-Simons theory

We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the quasiparticle number is shown to arise quantum mechanically and to agree with Laughlin theory. We also point out the effective equivalence of this model, and therefore of the quantum Hall system, with the Calogero model.Comment: 18 pages; final version to appear in JHE

Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory

We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the quantization of the inverse filling fraction and of the quasiparticle number, are reproduced by the quantum mechanics of the matrix model. We also point out that this system is holographically described in terms of the one-dimensional Sutherland integrable particle system.Comment: 25 pages; final version to appear in JHE