A-branes and Noncommutative Geometry

Details A-branes and Noncommutative Geometry A-branes and Noncommutative Geometry

2005-02-23

arxiv.org/abs/hep-th/0502212v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, latex

Scientific paper

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.

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