Abstract
We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized hypergeometric GKZ system which determines the off-shell superpotential and its analytic properties under deformation. Explicit expressions for the \( \mathcal{N} = 1 \) superpotential for families of type II/F-theory compactifications are obtained for a list of multi-parameter examples. Using the Hodge theoretic approach to open-string mirror symmetry, we obtain new predictions for integral disc invariants in the A model instanton expansion. We study the behavior of the brane vacua under extremal transitions between different Calabi-Yau spaces and observe that the web of Calabi-Yau vacua remains connected for a particular class of branes.
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Alim, M., Hecht, M., Jockers, H. et al. Type II/F-theory superpotentials with several deformations and \( \mathcal{N} = 1 \) mirror symmetry. J. High Energ. Phys. 2011, 103 (2011). https://doi.org/10.1007/JHEP06(2011)103
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DOI: https://doi.org/10.1007/JHEP06(2011)103