The Geometry of D-Brane Superpotentials

Details The Geometry of D-Brane Superpotentials The Geometry of D-Brane Superpotentials

2009-09-11

arxiv.org/abs/0909.2245v2

JHEP 1112 (2011) 060

Physics

High Energy Physics

High Energy Physics - Theory

v2: 30 pages, harvmac; appendix added, reference added, typos corrected

Scientific paper

10.1007/JHEP12(2011)060

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.

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