TITLE: Role for generalized geometries in string theory
QUESTION [9 upvotes]: What role do generalized geometries (in terms of Dirac structures, for instance, symplectic, Poisson, complex, and generalized complex structures in the sense of Hitchin, Cavalcanti, and Gualtieri) play in string theory?
EDIT: More generally, what role to Dirac structures (subbundles of the generalized tangent bundle $TM \bigoplus T^*M$ which are maximally isotropic to the natural pairing and closed under the Courant bracket) play?

REPLY [2 votes]: I would like to add that generalized geometry in the sense of Hitchin is also a good framework for the notion of brane (a very important notion in what physicists call M-theory) and also T-dualities one of which is mirror symmetry. Especially I have read an article basically saying that the category of generalized Calabi-Yau manifolds provide a good canditate for the Homological Mirror Symmetry conjecture but I don't remember the article anymore, sorry, maybe José Figueroa-O'Farrill does remember. See also the question: Mirror symmetries for generalized geometries ?.
EDIT: The article I was searching is: http://arxiv.org/abs/1106.1747.