Five-Brane Superpotentials and Heterotic/F-theory Duality

TL;DR

This paper explores heterotic/F-theory duality, linking five-brane superpotentials to flux superpotentials in F-theory, and provides a method to compute five-brane superpotentials via dual Calabi-Yau fourfolds.

Contribution

It reformulates heterotic/F-theory duality by constructing non-Calabi-Yau threefolds and maps five-brane superpotentials to flux superpotentials in F-theory.

Findings

Explicit map between five-brane superpotential and F-theory flux superpotential.

Construction of dual Calabi-Yau fourfolds with four-form flux.

Method to compute five-brane superpotentials explicitly.

Abstract

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.