Hypercharge flux in heterotic compactifications

We study heterotic Calabi-Yau models with hypercharge flux breaking, where the visible $E_8$ gauge group is directly broken to the standard model group by a nonflat gauge bundle, rather than by a two-step process involving an intermediate grand unified theory and a Wilson line. It is shown that the required alternative $E_8$ embeddings of hypercharge, normalized as required for gauge unification, can be found and we classify these possibilities. However, for all but one of these embeddings we prove a general no-go theorem which asserts that no suitable geometry and vector bundle leading to a standard model spectrum can be found. Intuitively, this happens due to the large number of index conditions which have to be imposed in order to obtain a correct physical spectrum in the absence of an underlying grand unified theory.