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

TL;DR

This paper proves that noncommutative Maxwell-Chern-Simons theory is equivalent to a free theory for marginally noncommutative spacetimes, establishing a duality with the Self-Dual model and providing an explicit covariant mapping.

Contribution

It demonstrates the duality between noncommutative Maxwell-Chern-Simons theory and the Self-Dual model at first order in noncommutativity, including an explicit variable mapping.

Findings

Maxwell-Chern-Simons theory is free in marginally noncommutative spacetimes.

A covariant mapping between models is explicitly derived.

Duality holds to first order in the noncommutativity parameter.

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.