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We study a direct flux breaking scenario in $SO(32)$ heterotic string theoryon general Calabi-Yau threefolds. The direct flux breaking, corresponding tohypercharge flux breaking in the F-theory context, allows us to derive theStandard Model in general Calabi-Yau compactifications. We present a generalformula leading to the three generations of quarks and leptons and no chiralexotics in a background-independent way. As a concrete example, we show thethree-generation model on a complete intersection Calabi-Yau threefold.

$SO(32)$ heterotic standard model vacua in general Calabi-Yau compactifications