摘要翻译：
研究了具有复辛目标空间X的三维拓扑Sigma模型（Rozansky-Witten模型）中的边界条件和缺陷。我们证明了边界条件对应于X中具有复纤维的复拉格朗日子流形。边界条件集具有2-范畴的结构；这2类中的态射在物理上被解释为一维缺陷线，用不同的边界条件分隔部分边界。这个2-范畴是X的Z/2-分次导出范畴的范畴化；它还与矩阵分解的类别和变形量化的类别（对称单形类别的量化）有关。在附录中，我们用任意偶数度的形式描述了B-模型的变形和相关的品牌类别。
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英文标题：
《Three-dimensional topological field theory and symplectic algebraic
  geometry I》
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作者：
Anton Kapustin, Lev Rozansky, Natalia Saulina
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Quantum Algebra        量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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英文摘要：
  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 Z/2-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 the appendix we describe a deformation of the B-model and the associated category of branes by forms of arbitrary even degree.
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PDF链接：
https://arxiv.org/pdf/0810.5415