Technically Natural Cosmological Constant From Supersymmetric 6D Brane
  Backreaction
  We provide an explicit example of a higher-dimensional model describing a
non-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 is
the 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-stabilized
supersymmetric bulk coupled to non-supersymmetric matter localized on a
(3+1)-dimensional positive-tension brane. We use recent techniques for
calculating 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 is
the transfer of stabilizing flux between the bulk and the branes. The UV
completion of the model can arise at scales much larger than M, allowing the
calculation of quantum effects like the zero-point energy of very massive
particles in the vacuum. We find that brane-localized loops do not affect the
4D curvature at all, but bulk loops can. These can be estimated on general
grounds and we show that supersymmetry dictates that they generate curvatures
that are generically of order m_KK^4/M_p^2. For realistic applications this
points to a world with two supersymmetric extra dimensions, with supersymmetry
in 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 Standard
Model particles are brane-localized and not at all supersymmetric (implying in
particular no superpartners or the MSSM). We discuss how the model evades
various no-go theorems that would naively exclude it, and briefly outline
several striking observational implications for tests of gravity and at the
LHC.
