Constrained superpotentials in harmonic gauge theories with eight supercharges

We consider D-dimensional supersymmetric gauge theories with eight supercharges (D≤6, N=8) in the framework of harmonic superspaces. The effective Abelian low-energy action for D=5 contains the free and Chern-Simons terms. Effective N=8 superfield actions for D≤4 can be written in terms of superpotentials satisfying the superfield constraints and (6-D)-dimensional Laplace equations. The role of alternative harmonic structures is discussed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 2, pp. 324–331, August, 1999.