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August 2005 Open-string BRST cohomology for generalized complex branes
Anton Kapustin, Yi Li
Adv. Theor. Math. Phys. 9(4): 559-574 (August 2005).


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 $\mathrm{Ext}$ groups of holomorphic line bundles supported on complex submanifolds: while the usual method leads to a spectral sequence converging to the $\mathrm{Ext}$, our approach expresses the $\mathrm{Ext}$ 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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Anton Kapustin. Yi Li. "Open-string BRST cohomology for generalized complex branes." Adv. Theor. Math. Phys. 9 (4) 559 - 574, August 2005.


Published: August 2005
First available in Project Euclid: 3 April 2006

zbMATH: 1129.81083
MathSciNet: MR2201105

Rights: Copyright © 2005 International Press of Boston


Vol.9 • No. 4 • August 2005
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