De Sitter Vacua from Heterotic M-Theory

It is shown how metastable de Sitter vacua can arise from heterotic M-theory. The balancing of two inherent non-perturbative effects, open membrane instantons and gaugino condensation on the hidden boundary, which act with opposing forces on the interval length, lead in particular to a stabilization of this modulus. Supersymmetry is broken spontaneously in the resulting vacua. For rather small open membrane instanton determinants the supersymmetry breaking scale and gravitino masses can be brought down to the TeV scale. It turns out that this can be achieved in a controllable regime of the theory and without any fine-tuning. Non-trivial vector bundles on the hidden boundary are phenomenologically favored which leave a hidden unbroken gauge group of low rank like SU(3). In addition these de Sitter vacua possess non-vanishing charged scalar matter fields and therefore do not suffer from massless charged scalars as does the weakly coupled heterotic string. We discuss the role of the $H_{(0,3)}$ and $H_{(1,2)}$ flux components for a stabilization of all moduli. The latter component leading to non-K\"ahler background geometries