Global topological defects in extra dimensions and the brane world concept

Summary: "D-dimensional (Dgeq5) configurations with 4D Minkowski external space-time and global spherically symmetric topological defects in the extra dimensions are discussed in the context of the brane world concept. The defect is formed with a hedgehog-like set of scalar fields phi^i with a symmetry-breaking potential V depending on the magnitude phi^2=phi^iphi^i. All possible kinds of globally regular configurations are singled out without specifying the shape of V(phi). Regular configurations with Dgeq6 can reach infinite radii, end with a cylinder of finite radius or possess two regular centres. The warp factors of configurations with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the centre. All of them are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models."