3D and 4D noncommutative electromagnetic duality and the role of the slowly varying fields limit
We study classical noncommutative (NC) electromagnetic duality in both 3D and 4D space-times through the Seiberg-Witten (SW) map to all orders in theta. We evaluate the role of space-time dimensions, of the gauge coupling constant g^2 inversion, of the slowly varying fields (SVF) limit and of the rule theta --> g^2 *theta (where * is the Hodge duality operator), which was originally found in the 4D space-time. Among our results, a new scalar picture for NC electromagnetism to second order in theta is established, a formula which simplifies considerably the application of the SW map in 3D is presented and we show that the SVF limit has a crucial role in this duality starting from the third order in theta for any dimension: outside this limit the symmetry between theta and g^2 *theta is lost.