Equivalence of D-brane categories

D-膜类别的等价性

• 批准号: 5252068
• 负责人: Professor Dr. Duco van Straten
• 金额: --
• 依托单位: Arbeitsgruppe Algebraische Geometrie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2004-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5252068?language=en
• 关键词: Equivalence; brane; categories

According to Strominger, Yau and Zaslow, mirror symmetry of Calabi-Yau manifolds should be understood in terms dual torus fibrations. On the other hand, Kontsevich proposed to formulate mirror symmetry as an equivalence of Ao-categories, one based on holomorphic D-branes and the other on special Lagrangian D-branes. These objects should be interchanged under T-duality (Fourier-Makai transform). Even for the simplest cases where the Calabi-Yau is a torus, many important questions remain nanswered. Although recently there has been progress in understanding the structure of SYZ-fibrations for certain explicit Calabi-Yau spaces, one is far from understanding the behaviour of the corresponding D-brane-categories. The purpose of the project is to find a general formulation for categorical mirror symmetry, encompassing, and to prove as much as possible for the simplest Calabi-Yau spaces like tori and quotients thereof.

根据Strominger、Yau和Zaslow的观点，Calabi-Yau流形的镜像对称性应该用对偶环面纤颤来理解。另一方面，Kontsevich提出将镜像对称性表示为Ao-范畴的等价，一个等价于全纯D-膜，另一个等价于特殊的Lagrangian D-膜。这些对象应该在T-对偶(傅立叶-马凯变换)下互换。即使在最简单的情况下，Calabi-Yau是一个环面，许多重要的问题仍然没有答案。虽然最近在理解某些显式Calabi-Yau空间的Syz-Bfiting的结构方面取得了进展，但人们对相应的D-膜范畴的行为的理解还远远不够。这个项目的目的是找到一个包含范畴镜像对称的一般公式，并尽可能多地证明最简单的Calabi-Yau空间，如环面及其商。