  Strongly coupled heterotic $E_8\times E_8$ string theory, compactified to
four dimensions on a large Calabi-Yau manifold ${\bf X}$, 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 ${\bf R}^4\times{\bf S}^1/{\bf Z}_2\times{\bf X}$, with the two
$E_8$'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 ${\bf S}^1/{\bf Z}_2$. 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.

High Energy Physics - Theory;High Energy Physics - Phenomenology