Kapustin, Anton and Li, Yi (2005) Openstring BRST cohomology for generalized complex branes. Advances in Theoretical and Mathematical Physics, 9 (4). pp. 559574. ISSN 10950761. http://resolver.caltech.edu/CaltechAUTHORS:KAPatmp05

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Abstract
It has been shown recently that the geometry of Dbranes in general topologically twisted (2,2) sigmamodels can be described in the language of generalized complex (GC) structures. On general grounds, such Dbranes (called GC branes) must form a category. We compute the BRST cohomology of open strings with both ends on the same GC brane. In mathematical terms, we determine spaces of endomorphisms in the category of GC branes. We find that the BRST cohomology can be expressed as the cohomology of a Lie algebroid canonically associated to any GC brane. In the special case of Bbranes, this leads to an apparently new way to compute Ext groups of holomorphic line bundles supported on complex submanifolds: while the usual method leads to a spectral sequence converging to the Ext, our approach expresses the Ext group as the cohomology of a certain differential acting on the space of smooth sections of a graded vector bundle on the submanifold. In the case of coisotropic Abranes, our computation confirms a proposal of Orlov and one of the authors (A.K.).
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Additional Information:  2005 © International Press of Boston. A.K. would like to thank Alexey Bondal, Andrei Căldăraru, Tony Pantev, and Marco Gualtieri for helpful discussions. Y.L. would like to thank YongGeun Oh for an interesting discussion. We are also grateful to the organizers of the Workshop on Mirror Symmetry at the Perimeter Institute, Waterloo, for providing a stimulating atmosphere. This work was supported in part by the DOE grant DEFG0392ER40701.  
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