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 M²_Pl~M²⁺ⁿ_*Lⁿ, we get two kinds of theories with TeV scale quantum gravity and submillimeter deviations from Newton's law. With M_*~TeV and L~submillimeter, we recover the phenomenology of theories with large extra dimensions. Alternatively, if M_*~L^-1~M_Pl, and our 3-brane is at a distance of ~100M^-1_Pl from the intersection, we obtain a theory with an exponential determination of the weak/Planck hierarchy.