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A-branes and Noncommutative Geometry

Kapustin, Anton (2005) A-branes and Noncommutative Geometry. . (Submitted)

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We argue that for a certain class of symplectic manifolds the category of A-branes (which includes the Fukaya category as a full subcategory) is equivalent to a noncommutative deformation of the category of B-branes (which is equivalent to the derived category of coherent sheaves) on the same manifold. This equivalence is different from Mirror Symmetry and arises from the Seiberg-Witten transform which relates gauge theories on commutative and noncommutative spaces. More generally, we argue that for certain generalized complex manifolds the category of generalized complex branes is equivalent to a noncommutative deformation of the derived category of coherent sheaves on the same manifold. We perform a simple test of our proposal in the case when the manifold in question is a symplectic torus.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Additional Information:(Submitted on 23 Feb 2005) February 1, 2008. I would like to thank Dima Orlov, Oren Ben-Bassat, Jonathan Block, Tony Pantev, and Marco Gualtieri for helpful discussions. I am also grateful to the organizers of the Workshop on Mirror Symmetry at the University of Miami 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
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Record Number:CaltechAUTHORS:20160511-075947917
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66970
Deposited By: Ruth Sustaita
Deposited On:11 May 2016 17:05
Last Modified:03 Oct 2019 10:01

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