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We provide an explicit example of a higher-dimensional model describing anon-supersymmetric spectrum of 4D particles of mass M, whose 4D geometry --{\em including loop effects} -- has a curvature that is of order R ~m_KK^4/M_p^2, where m_KK is the extra-dimensional Kaluza-Klein scale and M_p isthe 4D Planck constant. m_KK is stabilized and can in particular satisfy m_KK<< M. The system consists of a (5+1)-dimensional model with a flux-stabilizedsupersymmetric bulk coupled to non-supersymmetric matter localized on a(3+1)-dimensional positive-tension brane. We use recent techniques forcalculating how extra dimensions respond to changes in brane properties to show(at the classical level) that the low-energy 4D geometry is exactly flat,independent of the value of the brane tensions. Its mechanism for doing so isthe transfer of stabilizing flux between the bulk and the branes. The UVcompletion of the model can arise at scales much larger than M, allowing thecalculation of quantum effects like the zero-point energy of very massiveparticles in the vacuum. We find that brane-localized loops do not affect the4D curvature at all, but bulk loops can. These can be estimated on generalgrounds and we show that supersymmetry dictates that they generate curvaturesthat are generically of order m_KK^4/M_p^2. For realistic applications thispoints to a world with two supersymmetric extra dimensions, with supersymmetryin the bulk broken at the sub-eV KK scale - as proposed in hep-th/0304256 -requiring a 6D gravity scale somewhat higher than 10 TeV. Ordinary StandardModel particles are brane-localized and not at all supersymmetric (implying inparticular no superpartners or the MSSM). We discuss how the model evadesvarious no-go theorems that would naively exclude it, and briefly outlineseveral striking observational implications for tests of gravity and at theLHC.

Technically Natural Cosmological Constant From Supersymmetric 6D Brane Backreaction