The mathematics of the AdS/CFT correspondence

AdS/CFT 对应关系的数学

• 批准号: RGPIN-2016-03874
• 负责人: Costello, Kevin
• 金额: $ 4.01万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=690637
• 关键词: mathematics; AdS; CFT; correspondence

This project concerns the mathematics of string theory and quantum field theory. String theory is a putative "theory of everything", which has had a huge impact on mathematics. The very long-term goal of this project is to develop string theory as a discipline within mathematics. The more immediate, and very much attainable, goals are to develop mathematically a part of string theory (the part preserved by some supersymmetry), and to prove in this context certain string dualities. The project focuses on the AdS/CFT correspondence, which is a major topic in theoretical physics (with over 10,000 papers) but which has not been formulated mathematically (except in a few special cases). This project has many potential applications in algebraic geometry, geometric representation theory and related fields, which would be excellent projects for PhD and masters students.

该项目涉及弦理论和量子场论的数学。弦理论是一种假定的“万物理论”，对数学产生了巨大的影响。 该项目的长期目标是将弦理论发展为数学中的一门学科。更直接、更容易实现的目标是在数学上发展弦理论的一部分（由某些超对称性保留的部分），并在这种情况下证明某些弦对偶性。 该项目重点关注 AdS/CFT 对应关系，这是理论物理中的一个主要主题（有超过 10,000 篇论文），但尚未用数学公式表示（少数特殊情况除外）。该项目在代数几何、几何表示理论及相关领域具有许多潜在的应用前景，对于博士生和硕士生来说是一个很好的项目。