Quiver Gauge Theory, String Theory and Quantum Field Theory.

学生将学习颤振规范理论的主题，并尝试扩展这门课关于8个超对称规范理论的知识。近年来，为了更好地理解各种量子规范理论的模空间的几何性质，人们使用了颤振规范理论的技术；Hasse图，单极子公式，颤振减法和加法，离散测量和hyper-Kähler商，以及三维镜像对称就是这样的例子。箭囊规范理论对数学也有重要的意义——箭囊的语言提供了一种不同的探索几何空间的渠道，并且通常为数学家的形式化方法提供了不同的视角。在过去的几年里，微囊被用于研究诸如三维、五维和六维的规范理论。在相关的膜设置中，Hanany-Witten跃迁用于理解不同的相及其相关的物理特性。目前的工作包括扩展到六维的“负膜”设置，hyper-Kähler商和离散测量，扩展对不同理论的模空间如何相互关联的理解。

The student will study topics in quiver gauge theory and will attempt to expand the knowledge on this class of supersymmetric gauge theories with 8 supercharges.The techniques of quiver gauge theory have been used in recent years to better understand the geometry of the moduli space of various quantum gauge theories; Hasse diagrams, the monopole formula, quiver subtraction and addition, discrete gauging and hyper-Kähler quotients, and 3d mirror symmetry are some such examples.Quiver gauge theory also has important implications for mathematics - the language of quivers provides a different channel to probe geometric spaces and often offers a different perspective to the formal approach of the mathematician.In the past few years, quivers have been used to study gauge theories in, for example, three, five and six dimensions. In the associated brane setups, the Hanany-Witten transition is used to understand different phases and their associated physics. Current work includes extensions to the 'negative brane' setup in six dimensions, hyper-Kähler quotients and discrete gauging, expanding understanding of how the moduli spaces of different theories relate to each other.