  We show that in a general hidden sector model, supersymmetry breaking
necessarily generates at one-loop a scalar and gaugino mass as a consequence of
the super-Weyl anomaly. We study a scenario in which this contribution
dominates. We consider the Standard Model particles to be localized on a
(3+1)-dimensional subspace or ``3-brane'' of a higher dimensional spacetime,
while supersymmetry breaking occurs off the 3-brane, either in the bulk or on
another 3-brane. At least one extra dimension is assumed to be compactified
roughly one to two orders of magnitude below the four-dimensional Planck scale.
This framework is phenomenologically very attractive; it introduces new
possibilities for solving the supersymmetric flavor problem, the gaugino mass
problem, the supersymmetric CP problem, and the mu-problem. Furthermore, the
compactification scale can be consistent with a unification of gauge and
gravitational couplings. We demonstrate these claims in a four-dimensional
effective theory below the compactification scale that incorporates the
relevant features of the underlying higher dimensional theory and the
contribution of the super-Weyl anomaly. Naturalness constraints follow not only
from symmetries but also from the higher dimensional origins of the theory. We
also introduce additional bulk contributions to the MSSM soft masses. This
scenario is very predictive: the gaugino masses, squark masses, and $A$ terms
are given in terms of MSSM renormalization group functions.
