Issues on 3D noncommutative electromagnetic duality

We extend the ordinary 3D electromagnetic duality to the noncommutative (NC) space-time through a Seiberg-Witten map to second order in the noncommutativity parameter theta, defining a new scalar field model. There are similarities with the 4D NC duality; these are exploited to clarify properties of both cases. Up to second order in theta, we find that duality interchanges the 2-form theta with its 1-form Hodge dual (star)theta times the gauge coupling constant, i.e., theta ->(star)theta g(2) (similar to the 4D NC electromagnetic duality). We directly prove that this property is false in the third order expansion in both 3D and 4D space-times, unless the slowly varying fields limit is imposed. Outside this limit, starting from the third order expansion, theta cannot be rescaled to attain an S-duality. In addition to possible applications on effective models, the 3D space-time is useful for studying general properties of NC theories. In particular, in this dimension, we deduce an expression that significantly simplifies the Seiberg-Witten mapped Lagrangian to all orders in theta.