Topics in Quiver Gauge Theories

某些超对称规范理论的数据可以包含在一个称为“图”的图中。我们的目标是研究在不同维度和不同超对称性下的各种超规范理论的模空间（真空）。希格斯的希尔伯特级数和超规范理论的库仑分支使我们能够理解参数化这些模空间的规范不变算子。这些通常是代数变种，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。计算希格斯和库仑分支的希尔伯特级数，并从这些理论中解释物理或数学，将是该项目的一个大焦点。希格斯和库仑分支的动力学可以使用弦理论的膜结构来实现。对偶对称性，例如3d镜像对称性，被实现为膜，并将希格斯和库仑分支联系在一起。这将是这个项目的一个目标，更好地理解某些作为膜系统的规范理论。

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.