Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models

The compactification from the eleven-dimensional Ho\v{r}ava-Witten orbifold to five-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as specific $SU(4)$ vector bundle leading "heterotic standard model" in observable sector. Within context of strongly coupled M-theory, formalism for consistent hidden-sector bundles associated with single line presented, and introduced concrete example. Anomaly cancellation bulk space five-branes are discussed this context, constraint that hidden sector be compatible slope-stability requirements gauge bundle. further four-dimensional effective theory linearized BPS double domain wall then presented order $\kappa_{11}^{4/3}$. Specifically, generic constraints required anomaly restrictions imposed by positive squared couplings $\kappa_{11}^{4/3}$ detail. Three additional imposed, one guaranteeing $S^{1}/{\mathbb{Z}}_{2}$ length sufficiently larger than average radius, two enforcing both unification mass scale unified coupling $SO(10)$ group Finally, expression Fayet-Iliopoulos term an anomalous $U(1)$ symmetry its role $N=1$ supersymmetry low-energy discussed. It shown can preserved cancelling tree-level genus-one contributions against each another.