  In arXiv:1008.1018 it is shown that a given stable vector bundle $V$ on a
Calabi-Yau threefold $X$ which satisfies $c_2(X)=c_2(V)$ can be deformed to a
solution of the Strominger system and the equations of motion of heterotic
string theory. In this note we extend this result to the polystable case and
construct explicit examples of polystable bundles on elliptically fibered
Calabi-Yau threefolds where it applies. The polystable bundle is given by a
spectral cover bundle, for the visible sector, and a suitably chosen bundle,
for the hidden sector. This provides a new class of heterotic flux
compactifications via non-Kahler deformation of Calabi-Yau geometries with
polystable bundles. As an application, we obtain examples of non-Kahler
deformations of some three generation GUT models.
