| Abstract: | We review the construction of  off‐shell Poincaré supergravity in five dimensions. We describe in detail the minimal multiplet, which is the basic building block, containing the propagating fields of supergravity. All matter multiplets containing (8 + 8) components, being the smallest matter multiplets in five dimensions, are constructed. Using these multiplets the complete tensor calculus for supergravity is developed. As expected it turns out, that there exist three distinct minimal (i.e. containing (48 + 48) field components) off‐shell supergravities. The lagrangians for these theories and their gauged variants are given explicitly. These results are used in the second part to develop a tensor calculus on the orbifold $S^1/\mathbb{Z}_2$ . Gauged supergravity on the orbifold $S^1/\mathbb{Z}_2$ with additional cosmological constants at the fixpoints, is constructed. This generalizes the work of Randall‐Sundrum to local supersymmetry. The developed tensor calculus is used to extend this model to include matter located at the fixpoints. Chiral and super Yang‐Mills multiplets at the fixpoints are considered. |
