The Geometry of D-Brane Superpotentials

TL;DR

This paper explores the geometric structure of D-brane superpotentials in string theory, revealing a duality that relates them to flux superpotentials on Calabi-Yau fourfolds, and demonstrating this with explicit examples.

Contribution

It introduces a geometric framework using Calabi-Yau fourfolds to understand D-brane superpotentials via string duality, connecting different computational approaches.

Findings

D-brane superpotentials relate to flux superpotentials on fourfolds.

Calabi-Yau fourfold geometry reproduces matrix factorization results.

The duality clarifies features of superpotential calculations in literature.

Abstract

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.