Supersymmetric bulk-brane coupling with odd gauge fields

JHEP0608:032,2006 Supersymmetric bulk-brane coupling in Horava-Witten and Randall-Sundrum scenarios, when considered in the orbifold (``upstairs'') picture, enjoys similar features: a modified Bianchi identity and a modified supersymmetry transformation for the ``orthogonal'' part of the gauge field. Using a toy model with a 5D vector multiplet in the bulk (like in Mirabelli-Peskin model, but with an \emph{odd} gauge field $A_m$), we explain how these features arise from the superfield formulation. We also show that the corresponding construction in the boundary (``downstairs'') picture requires introduction of a special ``compensator'' (super)field.