Gauge gravity duality and new geometrical structures

测量重力二元性和新的几何结构

• 批准号: 2277778
• 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: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2277778
• 关键词: Gauge; gravity; duality; new; geometrical

The project will focus on the implications of the gauge gravity correspondence for geometry. In particular, it implies a relationship between algebraic structures (such as Calabi-Yau algebras) on the one hand and new differential geometrical structures (extensions of Hitchin's notion of generalised geometry) on the other. One concrete conjecture is that the cyclic cohomology of the algebra is equal to a new generalisation of Dolbeault cohomololgy on the manifold. This will give new insight into topics ranging from Hilbert series of quiver theories, to topological strings, to black hole state counting, to new hyper-Kahler quotient constructions. The student will start by learning some of the basics of both sides of the physical correspondence, and the underlying mathematics, then focus on a number of new examples: these include marginal deformations of the general class of Ypq geometries, the Plich-Warner geometries and flows between Pilch-Warner and T11, and in particular, geometries dual to wrapped M5-brane theories.

该项目将重点研究规范重力对应对几何的影响。特别是，它一方面暗示了代数结构（例如卡拉比-丘代数）与新的微分几何结构（希钦广义几何概念的扩展）之间的关系。一个具体的猜想是，代数的循环上同调等于流形上 Dolbeault 上同调的新推广。这将为从希尔伯特系列箭袋理论、拓扑弦、黑洞状态计数到新的超卡勒商结构等主题提供新的见解。学生将首先学习物理对应两侧的一些基础知识和基础数学，然后关注一些新的例子：这些包括 Ypq 几何一般类的边缘变形、Plich-Warner 几何以及 Pilch-Warner 和 T11 之间的流动，特别是与包裹 M5 膜理论对偶的几何。