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

Noncommutative Maxwell–Chern–Simons theory in 3 dimensions is defined in terms of star product and noncommutative fields. The 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 θ. 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.