Topics in quiver gauge theories

学生将学习颤振规理论的公式和广泛应用。这些形成了一大类量子场论，通常需要额外的超对称性，并且存在于不同的时空维度中。它们的动力学可以通过在弦理论中嵌入它们的自由度来解释，使用扩展的“膜”状态。超对称限制了由此产生的模空间（真空）的几何形状，因此给出了某些经典几何形状的重要新结构和解释，特别是超kahler空间，包括特殊类别的奇点。这为物理学和数学的研究提供了极其丰富的资源。构造中的两个中心思想是对偶对称性的作用，将明显不同的理论与不同的对称性联系起来，以及连接模空间不同扇区的膜跃迁的概念。该项目将重点研究不同时空维度、不同超对称程度、不同规范群和全局对称性下的一系列颤振理论构建。

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.