Enlarging the Parameter Space of Heterotic M-Theory Flux Compactifications to Phenomenological Viability

Heterotic M-Theory is a promising candidate for that corner of M-theory which makes contact with the real world. However, while the theory requires one of its expansion parameters, $\epsilon$, to be perturbatively small, a successful phenomenology requires $\epsilon = {\cal O}(1)$. We show that the constraint to have small $\epsilon$ is actually unnecessary: instead of the original flux compactification background valid to linear order in $\epsilon$ one has to use its appropriate non-linear extension. The structure of the non-linear background which comprises field-theory corrections of all $\kappa^{2n/3}, n \ge 1$ orders is protected by supersymmetry. As an independent check we show explicitly that the tree-level cosmological constant vanishes. We also comment on singularities and the issue of chirality changing transitions for the non-linear background. This background is then applied to predict Newton's Constant for vacua with an M5 brane on the basis of a stabilization mechanism for all universal moduli. For the simplest vacua without M5 brane we obtain a correction to the lower bound on Newton's Constant which brings it in perfect agreement with the measured value