Topological strings on noncommutative manifolds

Details Topological strings on noncommutative manifolds Topological strings on noncommutative manifolds

2003-10-06

arxiv.org/abs/hep-th/0310057v4

Int.J.Geom.Meth.Mod.Phys. 1 (2004) 49-81

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, AMS latex. v2: a reference to a related work has been added. v3: An error in the discussion of the Fourier-Mukai tra

Scientific paper

We identify a deformation of the N=2 supersymmetric sigma model on a Calabi-Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.

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