Geometry, dualities and the string landscape

几何、二元性和弦景观

• 批准号: 2614576
• 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: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2614576
• 关键词: Geometry; dualities; string; landscape

String theory is a putative theory of quantum gravity that also has the potential to give a unified description of the particles and interactions that form the fundamental building blocks of the matter and forces in our universe. In addition, string theory has a remarkable set of duality symmetries.Since according to general relativity gravity is intrinsically a theory of geometry, these dualities have had important implications for mathematics. This project aims to bring together two important recent developments in string theory. Broadly, the first is a set of new notions of geometrical structure that appears in the string theory generalisation of Riemannian geometry and unifies the string theory degrees of freedom. The second is the study of the "string landscape", that is, the general question of which low-energy theories of particle physics can arise in string theory. Since supersymmetric string theories (and their duals, known as "M-theory") describe ten- or eleven-dimensional geometries, one must assume that part of spacetime is a small six- or seven-dimensional compact space in order to realise our own four-dimensional universe. The geometry of this "compactification space" strongly influences the nature of the low-energy theory. Thus, a central question in the string landscape programme is to understand the range of possible compact geometries, and their properties. The new developments in string geometry mean that we now have access to a much more complete set of backgrounds, and, crucially, have new tools for studying properties such as their "moduli" (geometrical deformations that cost little or no energy). Developing our understanding of these geometries, the connections to duality and the implications for and insights from the string landscape programme are the central goals of this proposal. The medium- to long-term goals of this research are gain new understanding of the nature of quantum gravity, the fundamental symmetries of string theory, and the possibility of finding realistic unified theories of gravity and quantum mechanics. There are also potentially new and intriguing implications for mathematics, notably string-motivated extension of notions of special holonomy and algebraic geometry.

弦理论是一种假定的量子引力理论，它也有可能对构成我们宇宙中物质和力的基本组成部分的粒子和相互作用给出统一的描述。此外，弦论有一组显著的对偶对称，因为根据广义相对论，引力本质上是一种几何理论，这些对偶对数学有着重要的意义。这个项目的目的是把弦理论的两个重要的最新发展结合起来。广义地说，第一个是一组新的几何结构概念，出现在黎曼几何的弦理论推广中，统一了弦理论的自由度。第二个是“弦景观”的研究，也就是说，哪些低能粒子物理学理论可以在弦理论中出现的一般问题。由于超对称弦理论（以及它们的分支，被称为“M理论”）描述的是10维或11维几何，为了实现我们自己的四维宇宙，我们必须假设时空的一部分是一个小的6维或7维紧致空间。这种“紧化空间”的几何形状强烈地影响了低能理论的性质。因此，弦景观计划的一个中心问题是理解可能的紧凑几何的范围及其性质。弦几何的新发展意味着我们现在可以获得一组更完整的背景，而且，至关重要的是，我们有了新的工具来研究它们的“模量”（消耗很少或不消耗能量的几何变形）等性质。发展我们对这些几何的理解，与二元性的联系，以及对弦景观计划的影响和见解，是这个建议的中心目标。这项研究的中长期目标是对量子引力的性质、弦理论的基本对称性以及找到引力和量子力学的现实统一理论的可能性有新的认识。也有潜在的新的和有趣的影响数学，特别是字符串动机的扩展概念的特殊完整性和代数几何。