کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1843572 | 1031560 | 2009 | 61 صفحه PDF | دانلود رایگان |
We study boundary conditions and defects in a three-dimensional topological sigma-model with a complex symplectic target space X (the Rozansky–Witten model). We show that boundary conditions correspond to complex Lagrangian submanifolds in X equipped with complex fibrations. The set of boundary conditions has the structure of a 2-category; morphisms in this 2-category are interpreted physically as one-dimensional defect lines separating parts of the boundary with different boundary conditions. This 2-category is a categorification of the Z2Z2-graded derived category of X; it is also related to categories of matrix factorizations and a categorification of deformation quantization (quantization of symmetric monoidal categories). In Appendix B we describe a deformation of the B-model and the associated category of branes by forms of arbitrary even degree.
Journal: Nuclear Physics B - Volume 816, Issue 3, 1 August 2009, Pages 295–355