Infinitely Large New Dimensions

We construct intersecting brane configurations in Anti-de-Sitter space localizing gravity to the intersection region, with any number n of extra dimensions. This allows us to construct two kinds of theories with infinitely large new dimensions, TeV scale quantum gravity and sub-millimeter deviations from Newton's Law. The effective 4D Planck scale MPl is determined in terms of the fundamental Planck scale M* and the AdS radius of curvature L via the familiar relation MPl2 ∼ M*2+n Ln; L acts as an effective radius of compactification for gravity on the intersection. Taking M* ∼ TeV and L ∼ sub-mm reproduces the phenomenology of theories with large extra dimensions. Alternately, taking M* ∼ L-1 ∼ MPl, and placing our 3-brane a distance ∼ 100MPl-1 away from the intersection gives us a theory with an exponential determination of the Weak/Planck hierarchy