Superfield description of effective theories on BPS domain walls

We derive the low-energy effective theory on the BPS domain wall in 4D N=1 global SUSY theories in terms of the 3D superfields. Our derivation makes the preserved SUSY by the wall manifest and the procedure for integrating out the massive modes easier. Our procedure clarifies how the 3D superfields are embedded into the 4D chiral and vector superfields. We also point out a shortcoming of the conventional procedure for deriving the effective theory on the wall