Canonical functions, differential graded symplectic pairs in supergeometry, and Alexandrov-Kontsevich-Schwartz-Zaboronsky sigma models with boundaries
Canonical functions, differential graded symplectic pairs in supergeometry, and Alexandrov-Kontsevich-Schwartz-Zaboronsky sigma models with boundaries
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DOI：
10.1063/1.4900834
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发表时间：
2014-11
影响因子：
1.3
通讯作者：
N. Ikeda;Xiaomeng Xu
中科院分区：
文献类型：
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作者：
N. Ikeda;Xiaomeng Xu
分析了 Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma 模型的一致边界条件和相应的边界理论。作为它们的数学结构，我们在分级辛几何、正则函数和 QP 对方面引入了微分分级辛流形的推广，称为扭曲 QP 流形。我们将拓扑 sigma 模型的 AKSZ 构造推广到带有 Wess-Zumino 项的 sigma 模型，并表明文献中已知的所有扭曲类泊松结构实际上都可以自然地实现为 AKSZ sigma 模型的边界条件。
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structures, we introduce a generalization of differential graded symplectic manifolds, called twisted QP manifolds, in terms of graded symplectic geometry, canonical functions, and QP pairs. We generalize the AKSZ construction of topological sigma models to sigma models with Wess-Zumino terms and show that all the twisted Poisson-like structures known in the literature can actually be naturally realized as boundary conditions for AKSZ sigma models.