Distributed SUSY breaking: dark energy, Newton’s law and the LHC

We identify the underlying symmetry mechanism that suppresses the low-energy effective 4D cosmological constant within some 6D supergravity models, generically leading to results suppressed by powers of the KK scale, mK K2, relative to the much larger size, m4, associated with mass-m particles localized in these models on codimension-2 branes. These models are examples for which the local conditions for unbroken supersymmetry can be satisfied locally everywhere within the extra dimensions, but are obstructed only by global conditions like flux quantization or by the mutual inconsistency of the boundary conditions required at the various branes. Consequently quantities (like vacuum energies) forbidden by supersymmetry cannot become nonzero until wavelengths of order the KK scale are integrated out, since only such long wavelength modes can see the entire space and so ‘know’ that supersymmetry has broken. We verify these arguments by extending earlier rugby-ball calculations of one-loop vacuum energies within these models to more general pairs of branes within two warped extra dimensions. For the Standard Model confined to one of two otherwise identical branes, the predicted effective 4D vacuum energy density is of order ρvac ⋍ C(mMg/4πMp)4 = C(5.6 × 10−5 eV)4, where Mg ≳ 10 TeV (corresponding to extra-dimensional size r ≲ 1 μm) and Mp = 2.44 × 1018 GeV are the 6D and 4D rationalized Planck scales, and m is the heaviest brane-localized particle. (For numerical purposes we take m to be the top-quark mass and take Mg as small as possible, consistent with energy-loss bounds from supernovae.) C is a constant depending on the details of the bulk spectrum, which could easily be of order 500 for each of hundreds of fields in the bulk. The value C ∼ 6 × 106 would give the observed Dark Energy density.