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Open-string BRST cohomology for generalized complex branes

Kapustin, Anton and Li, Yi (2005) Open-string BRST cohomology for generalized complex branes. Advances in Theoretical and Mathematical Physics, 9 (4). pp. 559-574. ISSN 1095-0761. doi:10.4310/ATMP.2005.v9.n4.a2.

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It has been shown recently that the geometry of D-branes in general topologically twisted (2,2) sigma-models can be described in the language of generalized complex (GC) structures. On general grounds, such D-branes (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 B-branes, 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 A-branes, our computation confirms a proposal of Orlov and one of the authors (A.K.).

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Kapustin, Anton0000-0003-3903-5158
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 Yong-Geun 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 DE-FG03-92-ER40701.
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Department of Energy (DOE)DE-FG03-92-ER40701
Issue or Number:4
Record Number:CaltechAUTHORS:KAPatmp05
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ID Code:12229
Deposited By: Archive Administrator
Deposited On:29 Oct 2008 23:36
Last Modified:08 Nov 2021 22:26

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