On the self-duality condition in Chern-Simons systems

It is shown that in the Higgs and Chern-Simons-Higgs (without the Maxwell term) systems the self-duality constraint on the scalar field (combined with the equations of motion) by itself leads to specific forms for the potential. Similar results are shown to hold also for the supersymmetric extensions of the theories written in terms of superfields. A supersymmetric self-duality constraint on the matter superfield is proposed which contains the bosonic one and leads to specific forms of superpotentials without invoking arguments based on an explicit N=2 supersymmetry. (author)