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

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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.