122 research outputs found
Noncommutative Chern-Simons terms and the noncommutative vacuum
It is pointed out that the space noncommutativity parameters 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
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