Softly Broken Supersymmetric Desert from Orbifold Compactification

TL;DR

The authors introduce a new mechanism for supersymmetry breaking via boundary conditions in a 5D orbifold, where a small twist angle $α$ generates SUSY breaking at the scale $α/R$ and yields a long energy desert with a softly broken MSSM between $1/R$ and $α/R$. They construct explicit 5D theories with gauge groups $SU(3)\times SU(2)\times U(1)$ and $SU(5)$, exploring both brane and bulk matter, and demonstrate how radiative electroweak symmetry breaking can be achieved within constrained regions of parameter space, with $m_{1/2}=\hat{α}$, $m_{h_u,h_d}^2=\hat{α}^2$, and μ$=\hat{γ}$ at the compactification scale. The framework naturally links the origin of SUSY breaking to Peccei–Quinn (or Higgs-sector) breaking, solving the μ problem and the SUSY flavor/CP problems, while predicting gaugino mass unification at $1/R$ and distinct phenomenology depending on matter localization. The SU(5) embedding preserves gauge coupling unification and can suppress dangerous proton decay operators, offering a unified geometric origin for SUSY and GUT breaking. Overall, the work provides a coherent, testable avenue for realizing softly broken supersymmetry over a large energy range and motivates further study of the origin of the small twist angle $α$ in higher-dimensional dynamics.

Abstract

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.