Supersymmetric large extra dimensions

In this thesis we examine the viability of a recent proposal, known as Supersymmetric Large Extra Dimensions (SLED), for solving both the cosmological constant and the hierarchy problems. Central to this proposal is the requirement of two large extra dimensions of size rc ∼ 10 microm together with a low value for the higher-dimensional scale of gravity, M* ∼ 10 TeV. In order not to run into immediate conflict with experiment, it is presumed that all fields of the Standard Model are confined to a four-dimensional domain wall (brane). A realization of the SLED idea is achieved by relying on the 6D supergravity of Nishino and Sezgin (NS), which is known to have 4D-flat compactifications.;When work on this thesis first began, there were many open questions which are now answered either partially or completely. In particular, we expand on the known solutions of NS supergravity, which now include: warped compactifications having either 4D de Sitter or 4D anti-de Sitter symmetry, static solutions with broken 4D Lorentz invariance, and time-dependent "scaling" solutions. We elucidate the connection between brane properties and the asymptotic form of bulk fields as they approach the brane. Marginal stability of the 4D-flat solutions is demonstrated for a broad range of boundary conditions. Given that the warped solutions of NS supergravity which we consider are singular at the brane locations, we present an explicit regularization procedure for dealing with these singularities. Finally, we derive general formulae for the one-loop quantum corrections for both massless and massive field in arbitrary dimensions, with an eye towards applying these results to NS supergravity.