Gluino condensation in strongly coupled heterotic string theory

Strongly coupled heterotic E(8)XE(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 R(4)xS(1)/Z(2)XX, 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 S-1/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.