On the energy crisis in noncommutative image model Original Research Article

We study the image system in image-dimensional noncommutative space with and without Chern–Simons term. Using the Seiberg–Witten map we convert the noncommutative image system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern–Simons-image model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an “energy crisis”. In addition we examine the noncommutative image system with a Chern–Simons interaction. In this case we find that when the theory is transformed by the Seiberg–Witten map it also presents the same instanton solution as the commutative Chern–Simons-image model.