Static solutions in the R-4 brane world - art. no. 104025

A simple five-dimensional brane world model is proposed, motivated by M the ory compactified on a six-dimensional manifold of small radius and an S-1/Z (2) of large radius. We include a leading-order higher curvature correction to the tree-level bulk action since in brans world scenarios the curvature scale in the bulk may be comparable to the five-dimensional Planck scale a nd, thus, higher curvature corrections may become important. As a tractable model of the bulk theory we consider pure gravity, including a (Ricci-scal ar)(4) correction to the Einstein-Hilbert action. In this model theory, aft er a conformal transformation to the Einstein frame, we numerically obtain static solutions, each of which consists of a positive tension brane and a negative tension brane. For these solutions, we obtain two relations betwee n the warp factor and the brans tensions. The existence of these relations implies that, contrary to the original Randall-Sundrum model, the so called radion is no longer a zero mode. We conclude that the tension of our brane should be negative and that fine-tuning of the tension of both branes is n ecessary for a large warp factor to explain the large hierarchy between the Planck scale and the electroweak scale.