Solution to the hierarchy problem with an infinitely large extra dimensionand moduli stabilization - art. no. 085006

We construct a class of solutions to Einstein's equations for dimensions gr eater than or equal to 6. These solutions are characterized by a non-trivia l warp factor and possess a non-compact extra dimension. We study in detail a simple model in six dimensions containing two four-branes. One of each b rane's four spatial directions is compactified. The hierarchy problem is re solved by the enormous difference between the warp factors at the positions of the two-branes, with the standard model fields residing on the brane wi th a small warp factor. Both branes can have positive tensions. Their posit ions, and the size of the compact dimension, are determined in terms of the fundamental parameters of the theory by a combination of two independent a nd comparable effects-an anisotropic contribution to the stress tensor of e ach brans from quantum fields residing on it and a contribution to the stre ss tensor from a bulk scalar field. One overall fine-tuning of the paramete rs of the theory is required - that for the cosmological constant.