Proeyen, \Supersymmetry in singular spaces," hep-th/0007044

We discuss supersymmetry in spaces with a boundary, i.e. singular spaces. In particular, we discuss the situation in ten and five dimensions. In both these cases we review the construction of supersymmetric domain wall actions situated at the boundary. These domain walls act as sources inducing a jump in the mass parameter (D=10) or gauge coupling constant (D=5). Despite these singularities, supersymmetry can be formulated, maintaining its role as a square root of translations in this singular space. In D=10 we discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C(p) (p = 0, 1,... 9) as the effective field theory of Type IIA/IIB superstring theory. The case of 8-branes is studied in detail using the new bulk & brane action. As an application of our results we derive a quantization of the mass parameter and the cosmological constant in string units. InD=5 the setup is designed for the application to theRandall–Sundrum(RS) scenario. Thepossibility of a supersymmetric RS scenario relies on the existence of a special domain-wall solution containing a warp factor with the correct asymptotic behaviour such that gravity is suppressed in the transverse direction. Whether or not such a domain-wall solution exists depends on the detailed properties of the scalar potential. Finally, we review the conformal approach as a way to construct general matter coupled supergravity theories and hence general scalar potentials.