  We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau
manifolds with line bundle gauge backgrounds. Infinite sets of models that
satisfy the Bianchi identities and flux quantization conditions can be
constructed by letting their background flux quanta grow without bound. Even
though we do not have a general proof, we find that all examples are at the
boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which
can be thought of as vanishing D-term conditions, cannot be satisfied inside
the Kaehler cone unless a growing number of scalar Vacuum Expectation Values
(VEVs) is switched on. As they are charged under various line bundles
simultaneously, the gauge background gets deformed by these VEVs to a
non-Abelian bundle. In general, our physical expectation is that such infinite
sets of models should be impossible, since they never seem to occur in exact
CFT constructions.
