Geometry, supersymmetry and flux backgrounds in string theory

弦理论中的几何、超对称和通量背景

• 批准号: 1708628
• 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: 2015
• 资助国家: 英国
• 起止时间: 2015 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1708628
• 关键词: Geometry; supersymmetry; flux; backgrounds; string

String theory is a putative grand unified theory of quantum gravity where the fundamental objects are loops rather than point particles. In addition to the metric of conventional Einstein gravity it includes a number of additional excitations known as "fluxes". Understanding the role these degrees of freedom play in string theory backgrounds is central both to understanding how low-energy particle physics may emerge from string theory and investigating the remarkable duality between gravitational and non-gravitational theories known as the AdS-CFT correspondence, specifically when there is preserved supersymmetry. Recent work has shown that supersymmetric backgrounds can be understood in terms of a new class of geometrical structures that generalised conventional notions of symplectic or complex geometry. The project will study these new structures and in particular how they capture aspects of the AdS-CFT correspondence. Of particular interest will be constructing new solutions corresponding to wrapped M5-branes and general D3-brane backgrounds. Key points will be to understand the moduli spaces of these structures, their relations to topological theories and BV algebras, and connections to a-maximisation. There are also important connections to differential and algebraic geometry.

弦理论是一种假定的量子引力大统一理论，其中基本物体是环而不是点粒子。除了常规爱因斯坦引力的度规之外，它还包括一些称为“通量”的附加激发。理解这些自由度在弦理论背景中所扮演的角色，对于理解低能粒子物理如何从弦理论中产生，以及研究引力理论和非引力理论之间的显著对偶性（AdS-CFT对应），特别是在保留超对称性的情况下，都是至关重要的。最近的研究表明，超对称背景可以用一类新的几何结构来理解，这种几何结构概括了辛几何或复几何的传统概念。该项目将研究这些新结构，特别是它们如何捕捉AdS-CFT对应的各个方面。特别感兴趣的将是构建新的解决方案，对应于缠绕的m5膜和一般的3d膜背景。重点将是理解这些结构的模空间，它们与拓扑理论和BV代数的关系，以及与a最大化的联系。它与微分几何和代数几何也有重要的联系。