Softly broken supersymmetric desert from orbifold compactification

A new viewpoint for the gauge hierarchy problem is proposed: compactification at a large scale, $1/R,$ leads to a low energy effective theory with supersymmetry softly broken at a much lower scale, $\alpha /R.\mathrm{}$ The hierarchy is induced by an extremely small angle $\alpha$ which appears in the orbifold compactification boundary conditions. The same orbifold boundary conditions break Peccei-Quinn symmetry, leading to a new solution to the $\mu$ problem. Explicit 5D theories are constructed with gauge groups $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right)\mathrm{}$ and $\mathrm{SU}\left(5\right),$ with matter in the bulk or on the brane, which lead to the (next-to) minimal supersymmetric standard model below the compactification scale. In all cases the soft supersymmetry-breaking and $\mu$ parameters originate from bulk kinetic energy terms, and are highly constrained. The supersymmetric flavor and $\mathrm{CP}$ problems are solved.