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Remarks on A-branes, mirror symmetry, and the Fukaya category. (English) Zbl 1029.81058

Summary: 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
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