A Solution to the Hierarchy Problem with an Infinitely Large Extra Dimension and Moduli Stabilization

Abstract

We construct a class of solutions to the Einstein's equations for dimensions greater than or equal to six. These solutions are characterized by a non-trivial 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 brane's four spatial directions is compactified. The hierarchy problem is resolved by the enormous difference between the warp factors at the positions of the two branes, with the standard model fields living on the brane with small warp factor. Both branes can have positive tensions. Their positions, and the size of the compact dimension are determined in terms of the fundamental parameters of the theory by a combination of two independent and comparable effects---an anisotropic contribution to the stress tensor of each brane from quantum fields living on it and a contribution to the stress tensor from a bulk scalar field. One overall fine tuning of the parameters of the theory is required ---that for the cosmological constant.