In this dissertation, the five-dimensional gauged supergravity on a manifold with boundary is analyzed.; First, I consider the Mirabelli and Peskin model, which is a globally supersymmetric theory on a flat five-dimensional space-time with boundary. I discuss supersymmetry of this model in various settings (in the orbifold and boundary pictures, off-shell and on-shell, in superfield and component formulations). I show how the Gibbons-Hawking-like terms (the "Y-terms"), which are necessary for supersymmetry in the boundary picture, arise naturally from the superfield formulation.; Then I discuss the case of the five-dimensional (on-shell) supergravity on a manifold with boundary, which is an analog of the (eleven-dimensional) Horava-Witten theory. I show that the supersymmetry algebra indicates the boundary conditions that are necessary for (local) supersymmetry. I present a boundary action that allows one to establish supersymmetry using only the minimum set of boundary conditions. I also show how the same results can be achieved in the orbifold picture.; The supergravity construction is then used to present the supersymmetric Randall-Sundrum scenario, generalized for the case of detuned branes (local supersymmetry imposes a certain bound on the brane tensions). The scenario is considered both in the "upstairs" (orbifold) and "downstairs" (boundary) pictures. Spontaneous supersymmetry breaking by boundary conditions (the Scherk-Schwarz mechanism) is analyzed.; Finally, I present coupling of the bulk supergravity fields to a brane-localized Goldstone fermion, which provides a model-independent description of the supersymmetry breaking by a brane-localized dynamics. The bound on the brane tensions is relaxed and all three choices for the effective cosmological constant (corresponding to the Minkowski, de Sitter and anti-de Sitter backgrounds) become available.
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