Supersymmetry of RS bulk and brane

We review the construction of actions with supersymmetry on spaces with a d omain wall. The latter objects act as sources inducing a jump in the gauge coupling constant. Despite these singularities, supersymmetry can be formul ated, maintaining its role as a square root of translations in this singula r space. The setup is designed for the application in five dimensions relat ed to the Randall-Sundrum (RS) scenario. The space has two domain walls. We discuss the solutions of the theory with fixed scalars and full preserved supersymmetry, in which case one of the branes can be pushed to infinity, a nd solutions where half of the supersymmetries are preserved.