Dimensional Reduction over Coset Spaces and Supersymmetry Breaking

We address the question of supersymmetry breaking of a higher dimensional supersymmetric theory due to coset space dimensional reduction. In particular we study a ten-dimensional supersymmetric $E_{8}$ gauge theory which is reduced over all six-dimensional coset spaces. We find that the original supersymmetry is completely broken in the process of dimensional reduction when the coset spaces are symmetric. On the contrary softly broken four-dimensional supersymmetric theories result when the coset spaces are non-symmetric. From our analysis two promising cases are emerging which lead to interesting GUTs with three fermion families in four dimensions, one being non-supersymmetric and the other softly broken supersymmetric.