Five-Brane Superpotentials and Heterotic/F-theory Duality

Understand

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.