  Building on the covariant supergraph techniques in 4D N = 2 harmonic
superspace, we develop a manifestly 5D N = 1 supersymmetric and gauge covariant
formalism to compute the one-loop effective action for a hypermultiplet coupled
to a background vector multiplet. As a simple application, we demonstrate the
generation of a supersymmetric Chern-Simons action at the quantum level, both
in the Coulomb and the non-Abelian phases. These superfield results are in
agreement with the earlier component considerations of Seiberg et al. Our
analysis suggests that similar calculations in terms of hybrid 4D superfields
or within the 5D projective superspace approach may allow one to extract
suitable formulations for the non-Abelian 5D supersymmetric Chern-Simons
theory.
