Solution to the hierarchy problem with an infinitely large extra dimension and moduli stabilization

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Abstract
We construct a class of solutions to Einstein’s equations for dimensions greater than or equal to 6. 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 residing on the brane with a 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 residing 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.