The intersecting brane world
The scales of the Standard Model correspond to the positions of domain wall intersections on a straight line in a noncompact two-dimensional extra space. The domain walls partition an Anti-de Sitter spacetime. We show that domain wall intersections mark the orthogonal intersections of 1-cycles winding around a rectangular compact space and a hierarchy of subspaces, and that the noncompact extra space of the model is a covering space. 4-branes wrap 1-cycles of the compact spaces and intersect orthogonally in 3-branes, upon which the particles propagate. We show that particles are located precisely at domain wall intersections in the covering space.