  The disk partition function of the open topological string computes the
spacetime superpotential for D-branes wrapping cycles of a compact Calabi-Yau
threefold. We use string duality to show that when appropriately formulated,
the problem admits a natural geometrization in terms of a non-compact
Calabi-Yau fourfold without D-branes. The duality relates the D-brane
superpotential to a flux superpotential on the fourfold. This sheds light on
several features of superpotential computations appearing in the literature, in
particular on the observation that Calabi-Yau fourfold geometry enters the
problem. In one of our examples, we show that the geometry of fourfolds also
reproduces the D-brane superpotentials obtained from matrix factorization
methods.
