  In this note we propose a generalization of heterotic/F-theory duality. We
introduce a set of non-compact building blocks which we glue together to reach
compact examples of generalized duality pairs. The F-theory building blocks
consist of non-compact elliptically fibered Calabi-Yau fourfolds which also
admit a K3 fibration. The compact elliptic model obtained by gluing need not
have a globally defined K3 fibration. By replacing the K3 fiber of each
F-theory building block with a T^2, we reach building blocks in a heterotic
dual vacuum which includes a position dependent dilaton and three-form flux.
These building blocks are glued together to reach a heterotic flux background.
We argue that in these vacua, the gauge fields of the heterotic string become
localized, and remain dynamical even when gravity decouples. This enables a
heterotic dual for the hyperflux GUT breaking mechanism which has recently
figured prominently in F-theory GUT models. We illustrate our general proposal
with some explicit examples.
