Maxwell-Chern-Simons Theory is Free for Marginally Noncommutative Spacetimes

Abstract

We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter ${\theta }^{\mu \nu }$, with ${\theta }^{0i}=0$. This shows that the former theory is free for marginally noncommutative spacetimes. A $\theta$-generalized covariant mapping between the variables of the two models in question has been derived explicitly, that converts one model to the other, including the symplectic structure and action.

Title modified, Slightly enlarged version, No change in math. content, Version to appear in Phys.Lett.B

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• Three dimensional noncommutative bosonization
• On The Complete Seiberg-Witten Map For Theories With Topological Terms
• Issues on 3D Noncommutative Electromagnetic Duality
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• New aspects of quantization of Jackiw-Pi model: field-antifield formalism and noncommutativity
• Higher-derivative $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric Maxwell-Chern-Simons theories at one loop in superspace
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms