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We review the compactification to five‐dimensional heterotic M‐theory on a Schoen Calabi–Yau threefold and the specific    S  U  (  4  )    vector bundle leading to the “heterotic standard model” in the observable sector. Within strongly coupled heterotic M‐theory, a formalism for consistent hidden‐sector bundles associated with a single line bundle is presented, and a specific line bundle is introduced as a concrete example. Anomaly cancellation and the associated bulk space five‐branes are discussed in this context, as is slope‐stability of both the observable and hidden sector bundles. The further compactification to a four‐dimensional effective theory on a linearized BPS double domain wall is then presented to order    κ  11   4  /  3    . Specifically, the generic constraints required for anomaly cancellation and the restrictions imposed by positive squared gauge couplings to order    κ  11   4  /  3are presented in detail. Three additional constraints are imposed, one guaranteeing that theS  1   /   Z  2orbifold length is sufficiently larger than the average Calabi–Yau radius, and two enforcing that the hidden sector be compatible with both the unification mass scale and unified gauge coupling of the    S  O  (  10  )    group in the observable sector. Finally, the expression for the Fayet–Iliopoulos term associated with an anomalous  U (1) symmetry is presented and its role in    N  =  1    supersymmetry in the low‐energy effective theory is discussed. It is shown that    N  =  1    supersymmetry can be preserved by cancelling the tree‐level and genus‐one contributions against each another. As a check on our results, we calculate several quantities to order    κ  11   6  /  3and show that they remain physically acceptable, and even improve, when computed to higher order.

Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models