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Remarks on A-branes, Mirror Symmetry, and the Fukaya category

Anton Kapustin·Dmitri Orlov
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Abstract

We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi-Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure of a foliated manifold with a transverse holomorphic structure. We argue that the Fukaya category must be enlarged with such objects for the Homological Mirror Symmetry conjecture to be true.

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Anton Kapustin, Dmitri Orlov. 2001-09-12. Remarks on A-branes, Mirror Symmetry, and the Fukaya category. https://doi.org/10.1016/s0393-0440(03)00026-3

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