A Note on Noncommutative Chern-Simons Theories

Abstract

The three dimensional Chern-Simons theory on $\rr^2_θ\times \rr$ is studied. Considering the gauge transformations under the group elements which are going to one at infinity, we show that under arbitrary (finite) gauge transformations action changes with an integer multiple of $2\pi$ {\it if}, the level of noncommutaitive Chern-Simons is {\it quantized}. We also briefly discuss the case of the noncommutaitve torus and some other possible extensions.

Latex file, 15 pages, no figures, v3: one reference added, typos in references fixed

References in corpus (6)

• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Komaba Lectures on Noncommutative Solitons and D-Branes
• On Level Quantization for the Noncommutative Chern-Simons Theory
• Absence of Higher Order Corrections to Noncommutative Chern-Simons Coupling
• Solitons in 2+1 Dimensional Non-Commutative Maxwell Chern-Simons Higgs Theories

Cited by in corpus (33)

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• The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach
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• Three-dimensional Noncommutative Gravity
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• LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System
• Noncommutative Chern-Simons Solitons
• Morita Duality and Large-N Limits
• Issues of duality on non-commutative manifolds: the {\it non-equivalence} between self-dual and topologically massive models
• Lorentz and CPT symmetries in commutative and noncommutative spacetime
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• Dynamics of Giant-Gravitons in the LLM geometry and the Fractional Quantum Hall Effect
• New point-like sources and a conducting surface in Maxwell-Chern-Simons electrodynamics
• Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope
• Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
• Lowest Landau level theory of the bosonic Jain states
• Higher order derivatives extension of Maxwell-Chern-Simons electrodynamics in the presence of field sources and material boundaries
• Quantum aspects of Seiberg-Witten map in noncommutative Chern-Simons theory
• Supersymmetric non-Abelian noncommutative Chern-Simons theory
• On the Meaning of the String-Inspired Noncommutativity and its Implications
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Noncommutative massive Thirring model in three-dimensional spacetime
• Higher derivative Chern-Simons extension in the noncommutative QED${}_3$
• Induced magnetic moment in noncommutative Chern-Simons scalar QED
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
• Noncommutative supersymmetric Chern-Simons-matter model
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• BTZ Black Hole Entropy from a Chern-Simons Matrix Model
• Radiative corrections to the Chern-Simons term at finite temperature in the noncommutative Chern-Simons-Higgs model
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly