SUSY breaking through compactification

We propose a new mechanism of spontaneous supersymmetry breaking, The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulting from this mechanism. One noteworthy feature is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously, The mechanism we propose also yields a variety of non-trivial vacuum structures depending on topology of compactified spaces and also on symmetries of Lagrangians.