Constrained superpotentials in harmonic gauge theories with eight supercharges

We consider D-dimensional supersymmetric gauge theories with eight supercha rges (D less than or equal to 6, N = 8) in the framework of harmonic supers paces. The effective Abelian low-energy action for D = 5 contains the free and Chern-Simons terms. Effective N = 8 superfield actions for D less than or equal to 4 can be written in terms of superpotentials satisfying the sup erfield constraints and (6-D)-dimensional Laplace equations. The role of al ternative harmonic structures is discussed.