Topics in quiver gauge theories

箭袋规范理论的主题

• 批准号: 2440080
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2440080
• 关键词: Topics; quiver; gauge; theories

The student will study the formulation and broad applications of quiver gauge theories. These form a large class of quantum field theories, usually required to have additional supersymmetry and existing in diverse spacetime dimensions. Their dynamics can be interpreted by embedding their degrees of freedom in string theory, using extended "brane" states. Supersymmetry constrains the geometry of the resulting moduli spaces (of vacua) and so gives important new constructions and interpretations of certain classic geometries, notably hyper-Kahler spaces, including particular classes of singularities. This has provided an extremely rich source of research in both physics and mathematics. Two central ideas in the constructions are the role of duality symmetries, relating apparently distinct theories with different symmetries, and the notion of brane transitions connecting different sectors of moduli space. The project will focus on a range of quiver theory constructions in different spacetime dimensions and degree of supersymmetry, with different gauge groups and global symmetries.

学生将学习规范理论的公式和广泛的应用。这些理论形成了一大类量子场论，通常需要有额外的超对称性，并且存在于不同的时空维度中。它们的动力学可以通过将它们的自由度嵌入弦理论，使用扩展的“膜”态来解释。超对称性限制了模空间（真空模空间）的几何结构，因此对某些经典几何，特别是超卡勒空间（hyper-Kahler spaces），包括特殊的奇点类，给出了重要的新构造和解释。这为物理学和数学的研究提供了极其丰富的资源。两个中心思想的建设是对偶对称性的作用，有关明显不同的理论与不同的对称性，并连接不同部门的模空间的膜转移的概念。该项目将侧重于在不同的时空维度和超对称度，不同的规范群和全球对称性的一系列量子理论的建设。