Noncommutative Maxwell-Chern-Simons theory, duality and a new noncommutative Chern-Simons theory in d=3

TL;DR

This paper explores noncommutative Maxwell-Chern-Simons theory in three dimensions, deriving dual actions, introducing a new noncommutative Chern-Simons model, and proposing a transformation between noncommuting and ordinary fields.

Contribution

It presents a duality framework for noncommutative Maxwell-Chern-Simons theory and introduces a novel noncommutative Chern-Simons action based on ordinary fields.

Findings

Dual action derived using a parent action approach.

A new noncommutative Chern-Simons action formulated.

Transformation between noncommuting and ordinary fields proposed.

Abstract

Noncommutative Maxwell-Chern-Simons theory in 3-dimensions is defined in terms of star product and noncommutative fields. Seiberg-Witten map is employed to write it in terms of ordinary fields. A parent action is introduced and the dual action is derived. For spatial noncommutativity it is studied up to second order in the noncommutativity parameter \theta. A new noncommutative Chern-Simons action is defined in terms of ordinary fields, inspired by the dual action. Moreover, a transformation between noncommuting and ordinary fields is proposed.