Remarks on A-branes, mirror symmetry, and the Fukaya category

[摘要] 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. (C) 2003 Elsevier Science B.V. All rights reserved.

[发布日期] 2003-10-01

[效力级别]  Proceedings Paper

[关键词] A-branes;mirror symmetry;the Fukaya category