The mathematics of generalised dualities in M-theory

M 理论中广义对偶性的数学

• 批准号: 2602430
• 金额: --
• 依托单位: Swansea University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2602430
• 关键词: mathematics; generalised; dualities; theory

Whilst many mysteries remain about M-theory, the leading candidate for the quantum resolution of Einstein's general relativity, its most provocative features are U-dualities. Dualities are deep relationships and equivalences between seemingly distinct systems. Our central motivation is to illuminate the richness of dualities by exposing their mathematical structures. Goals1. Develop a refined understanding of quantum aspects of generalised T-dualities in string theory employing the mathematical tools of geometric and/or deformation quantisation2. Provide a mathematical underpinning of novel Exceptional Drinfel'd Algebras (EDAs) postulated to described generalised dualities of M-theory.3. Exploit the relation between Poisson-Lie dualities and Quantum Groups to give a quantum perspective on string dualities 4. Develop a linkage between the generalised Yang-Baxter equations that arise in EDAs and theory of integrable modelsThis work fits in a number of research areas within the Mathematical Science theme of EPSRC. In particular progress will be relevant to Mathematical Physics (through the potential applications to the mathematical structures sitting behind the dualities of string theory and through the relationships to integrable models), Geometry and Topology (through the development of generalised parallelisations with Hitchin's generalised geometry and its extensions, including non-commutative geometry), Algebra (through understanding the quantum algebras related to the classical exceptional Drinfel'd algebra and algebraic structures related to the Yang-Baxter equation)

尽管关于爱因斯坦广义相对论量子分辨率的主要候选者--M理论仍有许多谜团，但它最具挑衅性的特征是U-二元性。二元性是看似截然不同的系统之间的深层关系和等价物。我们的中心动机是通过揭示二元性的数学结构来阐明它们的丰富性。进球1。利用几何和/或形变量化的数学工具，发展对弦理论中广义T-对偶的量子方面的精细理解2。为描述广义M-理论的特殊Drinfel‘d代数(EDAS)提供了一个数学基础。利用泊松-李对偶和量子群之间的关系，给出弦对偶的量子观点4.发展在EDAS中产生的广义杨-巴克斯特方程和可积模型理论之间的联系这项工作适合于EPSRC数学科学主题的一些研究领域。特别是数学物理(通过对弦理论对偶背后的数学结构的潜在应用，以及通过与可积模型的关系)，几何和拓扑学(通过发展与希钦的广义几何及其推广，包括非交换几何)，代数(通过了解与经典的例外Drinfel‘d代数有关的量子代数和与杨-巴克斯特方程有关的代数结构)