Modeling the fifth dimension with scalars and gravity - art. no. 046008

A method for obtaining solutions to the classical equations for scalars plu s gravity in five dimensions is applied to some recent suggestions for bran e-world phenomenology. The method involves only first order differential eq uations. It is inspired by gauged supergravity but does not require supersy mmetry. Our first application is a full nonlinear treatment of a recently s tudied stabilization mechanism for interbrane spacing. The spacing is uniqu ely determined after conventional fine-tuning to achieve a zero four-dimens ional cosmological constant. if the fine-tuning is imperfect, there are sol utions in which the four-dimensional branes are de Sitter or anti-de Sitter spacetimes. Our second application is a construction of smooth domain wall solutions which in a well-defined limit approach any desired array of shar ply localized positive-tension branes. As an offshoot of the analysis we su ggest a construction of a supergravity c function for nonsupersymmetric fou r-dimensional renormalization group flows. The equations for fluctuations a bout an arbitrary scalar-gravity background are also studied. It is shown t hat all models in which the fifth dimension is effectively compactified con tain a massless graviton. The graviton is the constant mode in the fifth di mension. The separated wave equation can br recast into the form of supersy mmetric quantum mechanics. The graviton wave function is then the supersymm etric ground state, and there are no tachyons.