On duality of the noncommutative extension of the Maxwell-Chern-Simons model

TL;DR

This paper explores duality in noncommutative 3D field theories, deriving the noncommutative Self-Dual model via the Seiberg-Witten map and establishing its duality with a modified Maxwell-Chern-Simons theory.

Contribution

It introduces a noncommutative extension of the Self-Dual model and demonstrates its duality with a noncommutative Maxwell-Chern-Simons theory using the dual projection technique.

Findings

Established duality between noncommutative Self-Dual and Maxwell-Chern-Simons models.

Derived the noncommutative extension of the Self-Dual model via Seiberg-Witten map.

Verified algebraic and equation-of-motion equivalences in the noncommutative setting.

Abstract

We study issues of duality in 3D field theory models over a canonical noncommutative spacetime and obtain the noncommutative extension of the Self-Dual model induced by the Seiberg-Witten map. We apply the dual projection technique to uncover some properties of the noncommutative Maxwell-Chern-Simons theory up to first-order in the noncommutative parameter. A duality between this theory and a model similar to the ordinary self-dual model is estabilished. The correspondence of the basic fields is obtained and the equivalence of algebras and equations of motion are directly verified. We also comment on previous results in this subject.