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Disk Instantons, Mirror Symmetry and the Duality Web

Mina Aganagic·Albrecht Klemm·Cumrun Vafa
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Abstract

We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of ``flat coordinates'' for the boundary theory. We also discover an integer IR ambiguity needed to define the quantum theory of D-branes wrapped over non-compact Lagrangian submanifolds. In the large $N$ dual Chern-Simons theory, this ambiguity is mapped to the UV choice of the framing of the knot. In a type IIB dual description involving $(p,q)$ 5-branes, disk instantons of type IIA get mapped to $(p,q)$ string instantons. The M-theory lift of these results lead to computation of superpotential terms generated by M2 brane instantons wrapped over 3-cycles of certain manifolds of $G_2$ holonomy.

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Mina Aganagic, Albrecht Klemm, Cumrun Vafa. 2001-05-04. Disk Instantons, Mirror Symmetry and the Duality Web. https://doi.org/10.1515/zna-2002-1-201

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