Harmonic superpotentials and symmetries in gauge theories with eight supercharges Original Research Article

Models of interactions of D-dimensional hypermultiplets and supersymmetric gauge multiplets with N = 8 supercharges (D ⩽ 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 in introduced for a description of l 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, N = 8 supermultiplets are solved with the help of the SU(2) × Spin(5) harmonics. Effective gauge actions in the full D ⩽ 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.