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, α/R. The hierarchy is induced by an extremely small angle α which appears in the orbifold compactification boundary conditions. The same orbifold boundary conditions break Peccei-Quinn symmetry, leading to a new solution to the μ problem. Explicit 5d theories are constructed with gauge groups SU(3) × SU(2) × U(1) and SU(5), 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 μ parameters originate from bulk kinetic energy terms, and are highly constrained. The supersymmetric flavor and CP problems are solved.