Infinite hidden symmetries and integrability of N=4 super-Yang-Mills theory

N=4超杨-米尔斯理论的无限隐对称性与可积性

• 批准号: 446925065
• 负责人: Professor Dr. Olaf Lechtenfeld
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/446925065?language=en
• 关键词: Infinite; hidden; symmetries; integrability; N=4

We are witnessing an increasing role of algebro-geometric methods in the worldwide study of strings, gauge theories and integrable models. Me and my collaborators have participated in this endeavors through the investigation of N=2 strings and their hidden Kac-Moody type symmetries, of topological strings on supertwistor spaces and the corresponding string field theories, of holomorphic Chern-Simons and super-Yang-Mills theories, as well as of integrable models in lower dimensions. Our studies have given us far-reaching experience with twistor methods, differential geometry, extended supersymmetry and integrability. This competence will be further employed to an improved handling of the infinite hidden symmetries of N=4 supersymmetric Yang-Mills theory.The present project intends to elaborate the twistor description of N=4 super-Yang-Mills theory and its self-dual subsector from the viewpoint of Poisson geometry, Poisson-Lie groups and dressing transformations. The consideration of N=4 super-Yang-Mills theory by twistor methods combined with the methods of Poisson geometry and Poisson-Lie groups remains yet unaddressed. We intend to fill this gap and to study hidden Poisson-Lie symmetries of N=4 supersymmetric Yang-Mills theory.

我们见证了代数几何方法在弦、规范理论和可积模型的全球研究中的作用越来越大。我和我的合作者通过研究N=2弦及其隐藏的Kac-Moody对称性、超扭曲空间上的拓扑弦和相应的弦场理论、全纯Chern-Simons理论和超杨-Mills理论，以及低维的可积模型，参与了这项工作。我们的研究给了我们在扭曲方法、微分几何、扩展的超对称性和可积性方面的深远经验。这一能力将被进一步用于改进对N=4超对称Yang-Mills理论无限隐藏对称性的处理。本项目旨在从泊松几何、Poisson-Lie群和Dressing变换的角度阐述N=4超Yang-Mills理论及其自对偶子部分的扭曲描述。用扭曲方法结合泊松几何和泊松-李群的方法来考虑N=4个超杨-米尔斯理论的问题尚未得到解决。我们打算填补这一空白，并研究N=4超对称杨-米尔斯理论的隐藏泊松-李对称性。