Infinitely large new dimensions

We construct intersecting brane configurations in anit-de Sitter (AdS) space which localize gravity to the intersection region, generalizing the trapping of gravity to any number n of infinite extra dimensions. Since the 4D Planck scale M-Pl is determined by the fundamental Planck scale M-* and the AdS radius L via the familiar relation M-Pl(2) similar to M-*(2+n) L-n we get two kinds of theories with TeV scale quantum gravity and submillimeter deviations from Newton's law. With M-* similar to TeV and L similar to submillimeter, we recover the phenomenology of theories with large extra dimensions; Alternatively, if M-* similar to L similar to M-Pl, and our 3-brane is at a distance of similar to 100M(Pl)(-1) from the intersection, we obtain a theory with an exponential determination of the weak/Planck hierarchy.