Harmonic superpotentials and symmetries in gauge theories with eight supercharges

Models of interactions of D-dimensional hypermultiplets and supersymmetric gauge multiplets with N = 8 supercharges (D less than or equal to 6) can be formulated in the framework of harmonic superspaces. The effective Coulomb low-energy action for D = 5 includes the free and Chern-Simons terms. We consider also the non-abelian superfield D = 5 Chern-Simons action. The biharmonic D = 3, N = 8 superspace is introduced for a description of 1 and r supermultiplets and the mirror symmetry. The D = 2, (4,4) gauge theory and hypermultiplet interactions are considered in the triharmonic superspace. Constraints for D = 1, ni = 8 supermultiplets are solved with the help of the SU(2)x Spin(S) harmonics. Effective gauge actions in the full D less than or equal to 3, N = 8 superspaces contain constrained (harmonic) superpotentials satisfying the (6 - D) Laplace equations for the gauge group U(1) or corresponding (6 - D)p-dimensional equations for the gauge groups [U(1)](P). Generalized harmonic representations of superpotentials connect equivalent superfield structures of these theories in the full and analytic superspaces. The harmonic approach simplifies the proofs of non-renormalization theorems. (C) 1999 Published by Elsevier Science B.V. All rights reserved.