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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 αwhich appears in the orbifold compactification boundary conditions. The same orbifold boundary conditions break Peccei-Quinn symmetry, leading to a new solution to the μproblem. Explicit 5d theories are constructed with gauge groups SU(3) \times SU(2) \times 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 μparameters originate from bulk kinetic energy terms, and are highly constrained. The supersymmetric flavor and CP problems are solved.