Coisotropic Branes, Noncommutativity, and the Mirror Correspondence

Abstract

We study coisotropic A-branes in the sigma model on a four-torus by explicitly constructing examples. We find that morphisms between coisotropic branes can be equated with a fundamental representation of the noncommutatively deformed algebra of functions on the intersection. The noncommutativity parameter is expressed in terms of the bundles on the branes. We conjecture these findings hold in general. To check mirror symmetry, we verify that the dimensions of morphism spaces are equal to the corresponding dimensions of morphisms between mirror objects.

13 pages

References in corpus (3)

• Remarks on A-branes, Mirror Symmetry, and the Fukaya category
• Homological mirror symmetry for the quartic surface
• Geometry of coisotropic submanifolds in symplectic and Kähler manifolds

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