Origami World

We paste together patches of $AdS_6$ to find solutions which describe two4-branes intersecting on a 3-brane with non-zero tension. We constructexplicitly brane arrays with Minkowski, de Sitter and Anti-de Sitter geometriesintrinsic to the 3-brane, and describe how to generalize these solutions to thecase of $AdS_{4+n}$, $n>2$, where $n$ $n+2$-branes intersect on a 3-brane. TheMinkowski and de Sitter solutions localize gravity to the intersection, leadingto 4D Newtonian gravity at large distances. We show this explicitly in the caseof Minkowski origami by finding the zero-mode graviton, and computing thecouplings of the bulk gravitons to the matter on the intersection. In de Sittercase, this follows from the finiteness of the bulk volume. The effective 4DPlanck scale depends on the square of the fundamental 6D Planck scale, the$AdS_6$ radius and the angles between the 4-branes and the radial $AdS$direction, and for the Minkowski origami it is $M_4{}^2 = {2/3} \Bigl(\tan\alpha_1 + \tan \alpha_2 \Bigr) M_*{}^4 L^2$. If $M_* \sim {\rm few} \timesTeV$ this may account for the Planck-electroweak hierarchy even if $L \sim10^{-4} {\rm m}$, with a possibility for sub-millimeter corrections to theNewton's law. We comment on the early universe cosmology of such models.Comment: plain LaTeX, 23 pages + 2 .eps figure