Topics in Quiver Gauge Theories

箭袋规范理论主题

• 批准号: 2757471
• 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: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2757471
• 关键词: Topics; Quiver; Gauge; Theories

The data of certain supersymmetric gauge theories can be contained in a diagram called a quiver. We aim to study the moduli space (of vacua) of various quiver gauge theories in different dimensions and with various amounts of supersymmetry.The Hilbert series of Higgs and Coulomb branches of quiver gauge theories allow us to understand the gauge invariant operators that parameterise these moduli spaces. These are often algebraic varieties such as (closures of) nilpotent orbits of classical and exceptional algebras. This has been interesting for both physicists and mathematicians. Computations of Hilbert series for Higgs and Coulomb branches of various quiver gauge theories and interpreting physics or mathematics from these would be a large focus of the project.The dynamics of quiver gauge theories can be realised using the brane construction from string theory. Duality symmetries such as 3d mirror symmetry, for example, are realised as branes and relate the Higgs and Coulomb branches of a quiver gauge theory. It would be a goal for this project, to better understand certain quiver gauge theories as a brane system.

某些超对称规范理论的数据可以包含在一个称为颤振的图中。我们的目的是研究不同维数和不同超对称量的各种颤振规范理论的模空间（真空）。颤振规范理论的希格斯和库仑分支的希尔伯特级数使我们能够理解参数化这些模空间的规范不变量算子。这些通常是代数的变种，例如经典代数和例外代数的幂零轨道的闭包。这对物理学家和数学家来说都很有趣。计算各种颤振规范理论的希格斯和库仑分支的希尔伯特级数，并从这些分支中解释物理或数学，将是该项目的一大重点。颤振规范理论的动力学可以用弦理论的膜结构来实现。例如，对偶对称性，如三维镜像对称，被实现为膜，并将颤振规范理论的希格斯和库仑分支联系起来。这将是这个项目的目标，以更好地理解某些颤振规范理论作为一个膜系统。