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 $M_{\mathrm{Pl}}$ is determined by the fundamental Planck scale $M_{*}$ and the AdS radius $L$ via the familiar relation $M_{\mathrm{Pl}}^2\sim M_{*}^{2+n}{L}^n$, we get two kinds of theories with TeV scale quantum gravity and submillimeter deviations from Newton's law. With $M_{*}\sim \mathrm{TeV}$ and $L\sim \mathrm{sub}\mathrm{millimeter}$, we recover the phenomenology of theories with large extra dimensions. Alternatively, if $M_{*}\sim L^{-1\mathrm{}}\sim M_{\mathrm{Pl}}$, and our 3-brane is at a distance of $\sim {100M}_{\mathrm{Pl}}^{-1\mathrm{}}$ from the intersection, we obtain a theory with an exponential determination of the weak/Planck hierarchy.