### abstract

- We identify the underlying symmetry mechanism that suppresses the low-energy effective 4D cosmological constant within 6D supergravity models, leading to results suppressed by powers of the KK scale relative to the much larger masses associated with particles localized on codimension-2 branes. In these models the conditions for unbroken supersymmetry can be satisfied locally everywhere within the extra dimensions, but are obstructed by global conditions like flux quantization or the mutual inconsistency of boundary conditions at the various branes. Consequently quantities forbidden by supersymmetry cannot be nonzero until wavelengths of order the KK scale are integrated out, since only such long wavelength modes see the entire space and so know that supersymmetry breaks. We verify these arguments by extending earlier rugby-ball calculations of one-loop vacuum energies to more general pairs of branes within two warped extra dimensions. The predicted effective 4D vacuum energy density can be of order C (m Mg/4 pi Mp)^4, where Mg (Mp) is the rationalized 6D (4D) Planck scale and m is the heaviest brane-localized particle. Numerically this is C (5.6 x 10^{-5} eV)^4 if we take m = 173 GeV and take Mg as small as possible (10 TeV corresponding to KK size r < 1 micron), consistent with supernova bounds. C is a constant depending on details of the bulk spectrum, which could be ~ 500 for each of hundreds of fields. The value C ~ 6 x 10^6 gives the observed Dark Energy density.