Abstract
We consider the Maxwell–Chern–Simons theory in non-commutative three-dimensional space–time. We show that the Seiberg–Witten map is ambiguous due to the dimensional coupling constant. To get the dual theory we start from a master action obtained by promoting the global shift invariance to a local one. We also obtain the mapping between the observables of the two equivalent theories. We show that the equivalence between the Maxwell–Chern–Simons theory and the self-dual model in commutative space–time does not survive in the non-commutative setting.
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