Journal
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Volume 1, Issue 1-2, Pages 49-81Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219887804000034
Keywords
topological sigma-models; topological D-branes; noncommutative geometry
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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 hyperkdhler 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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