  Under heterotic/F-theory duality it was argued that a wide class of heterotic
five-branes is mapped into the geometry of an F-theory compactification
manifold. In four-dimensional compactifications this identifies a five-brane
wrapped on a curve in the base of an elliptically fibered Calabi-Yau threefold
with a specific F-theory Calabi-Yau fourfold containing the blow-up of the
five-brane curve. We argue that this duality can be reformulated by first
constructing a non-Calabi-Yau heterotic threefold by blowing up the curve of
the five-brane into a divisor with five-brane flux. Employing
heterotic/F-theory duality this leads us to the construction of a Calabi-Yau
fourfold and four-form flux. Moreover, we obtain an explicit map between the
five-brane superpotential and an F-theory flux superpotential. The map of the
open-closed deformation problem of a five-brane in a compact Calabi-Yau
threefold into a deformation problem of complex structures on a dual Calabi-Yau
fourfold with four-form flux provides a powerful tool to explicitly compute the
five-brane superpotential.
