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Topological strings in generalized complex space. (English) Zbl 1154.81024
The paper presents a topological sigma-model that depends only on a generalized complex structure of the target space (a generalized Calabi-Yau space). The formalism of M. Alexandrov, A. Schwarz, O. Zaboronsky and M. Kontsevich [Int. J. Mod. Phys. A 12, No. 7, 1405–1429 (1997; Zbl 1073.81655)], which is based on the Batalin-Vilkovisky construction, is employed. A study of the closed sector at the tree level without instanton corrections reproduces the observables and correlation functions found by S. Barannikov and M. Kontsevich [Int. Math. Res. Not. 1998, No. 4, 201–215 (1998; Zbl 0914.58004)] and Y. Li [On deformations of generalized complex structures: the generalized Calabi-Yau case,arXiv:hep-th/0508030v2)], identifies the extended moduli space and yields the familiar action of the twisted N=2 conformal field theory after gauge fixing. In the open sector a generalized complex structure represented by an ordinary complex structure and a holomorphic Poisson bivector is considered, whereby the product in the algebra of open strings is deformed into the non-commutative Kontsevich *-product.

MSC:
81T45 Topological field theories in quantum mechanics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32Q25 Calabi-Yau theory (complex-analytic aspects)
53C80 Applications of global differential geometry to the sciences
53D55 Deformation quantization, star products
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