G-Fluxes and Non-Perturbative Stabilisation of Heterotic M-Theory

We examine heterotic M-theory with a parallel M5 brane. After deriving the four-dimensional low-energy supergravity potential including open membrane instantons, gaugino condensation and M5 brane instantons, we focus on the first two non-perturbative effects. We find in the pure open membrane case, where the parallel M5 gets stabilized at the middle of the orbifold interval, that the vacuum energy is manifestly positive and that the orbifold-length and volume modulus are stabilized. Here, the leading terms of the potential vanish and it is essential to include all subleading corrections. In the pure gaugino condensation case the orbifold-length is stabilized, essentially from Kähler-potential terms, at small values and the M5 at the hidden boundary. Since the M5 looses then its influence on the running of the Calabi-Yau volume, the same stabilisation should occur if the M5 would be absent. Finally we combine both open membrane and gaugino condensation effects and show how the latter slightly modifies the dominant open membrane effects. For those vacua we determine the supersymmetry-breaking scale and the gravitino mass. [email protected] [email protected]