Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-02-04
Nucl.Phys. B554 (1999) 365-390; Erratum-ibid. B644 (2002) 405-406
Physics
High Energy Physics
High Energy Physics - Theory
Formulas of the non-Abelian Chern-Simons 5D action in Sect. 2 are corrected and the note with a new reference added
Scientific paper
10.1016/S0550-3213(99)00267-9
Models of interactions of D-dimensional hypermultiplets and supersymmetric gauge multiplets with $\cN=8$ supercharges $(D{\leq} 6)$ 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 $D=3,\cN=8$ superspace is 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 $D{=}1,\cN{=}8$ supermultiplets are solved with the help of the $SU(2){\times}Spin(5)$ harmonics. Effective gauge actions in the full $D{\leq}3,\cN{=}8$ 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.
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