Gluino condensation in strongly coupled heterotic string theory

Strongly coupled heterotic ${\mathrm{E}}_8$×${\mathrm{E}}_8$ string theory, compactified to four dimensions on a large Calabi-Yau manifold X, may represent a viable candidate for the description of low-energy particle phenomenology. In this regime, heterotic string theory is adequately described by low-energy $M$ theory on ${\mathbf{R}}^4$×${\mathbf{S}}^1$/${\mathbf{Z}}_2$×X, with the two ${\mathrm{E}}_8$'s supported at the two boundaries of the world. In this paper we study the effects of gluino condensation as a mechanism for supersymmetry breaking in this $M$--theory regime. We show that when a gluino condensate forms in $M$ theory, the conditions for unbroken supersymmetry can still be satisfied locally in the orbifold dimension ${\mathbf{S}}^1$/${\mathbf{Z}}_2$. Supersymmetry is then only broken by the global topology of the orbifold dimension, in a mechanism similar to the Casimir effect. This mechanism leads to a natural hierarchy of scales, and elucidates some aspects of heterotic string theory that might be relevant to the stabilization of moduli and the smallness of the cosmological constant.