  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 *theta times the gauge coupling
constant, i.e., theta --> *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.
