Non-abelian Structures in String Theory

弦论中的非阿贝尔结构

• 批准号: SAPIN-2016-00032
• 负责人: Karczmarek, Joanna
• 金额: $ 3.64万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=763020
• 关键词: Non; abelian; Structures; String; Theory

Einstein's theory of General Relativity describes gravitational forces between large objects: the attraction between the Earth and the Sun that holds the Earth in its orbit around the Sun, or the forces that have been determining the rate of expansion of the Universe since the Big Bang. General Relativity is an elegant and accurate theory and its predictions have been thoroughly tested by observations. Its central idea is that space and time are dynamical entities and gravity is nothing more than space-time being deformed.Quantum Mechanics is the theory of the small: the atom, as well as the atom's constituents. It governs everything from superconductivity to the speed of chemical reactions, from the behaviour of electrons to that of the recently discovered Higgs particle. Quantum theory predictions agree with experimental results to an unprecedented accuracy.General Relativity and Quantum Mechanics are the two paradigms through which we describe our Universe; however, it is not understood how to combine them into a single framework. We lack a unified approach to describing physical phenomena, and this limits our ability to study some of the most fascinating objects in the Universe (such as Black Holes) which are at once quantum mechanical and gravitational in nature.String Theory is currently our best candidate for a framework through which these two theories can be brought together. It has some profound consequences for what we think might be possible in our Universe, such as existence of extra dimensions. The details of how String Theory allows General Relativity and Quantum Mechanics to come together are not well understood: one idea is that space and time are not fundamental concepts, instead, space-time and its dynamics (i.e., gravity) might emerge from some microscopic degrees of freedom in a way similar to that in which movement of water emerges from the collective behaviour of a large number of water molecules. General Relativity, then, should emerge together with space-time from a Quantum Mechanical model of some objects more fundamental than space and time themselves. Such a formulation would be the ultimate theory of Quantum Gravity. Towards this goal, my work explores emergent geometries and their properties through String Theoretic tools.In this Proposal, I outline a research program bringing together several recent advancements in Quantum Gravity research such as holography, entanglement entropy, noncommutative geometry and matrix models. The central theme here is non-abelian objects: mathematical entities for which x times y is not the same as y times x, of which simplest example is square matrices. Such non-abelian entities appear in String Theory as coordinates of fundamental objects called D-branes, providing us with clues towards the true nature of space-time. Unravelling these clues is the main purpose of my work.

爱因斯坦的一般相对论理论描述了大物体之间的引力：地球与太阳之间的吸引力将地球固定在其围绕太阳周围的轨道上，或者自从大爆炸以来一直在确定宇宙膨胀速率的力量。一般相对论是一种优雅而准确的理论，其预测已通过观察进行了彻底的测试。它的核心思想是时空是动态的实体，而重力不过是时空变形。Quantum Mechanics是小的理论：原子和原子的成分。它控制着从超导性到化学反应速度的一切，从电子的行为到最近发现的希格斯粒子的行为。量子理论预测与实验结果相符，这是前所未有的准确性。一般相对论和量子力学是我们描述宇宙的两个范式。但是，尚不理解如何将它们组合到一个框架中。我们缺乏描述物理现象的统一方法，这限制了我们研究宇宙中一些最迷人的物体（例如黑洞）的能力，这些物质立即是量子机械和引力。对于可以通过这两种理论汇总在一起的框架。它对我们认为在宇宙中可能发生的可能性产生了深远的影响，例如额外的维度存在。字符串理论如何允许一般相对论和量子力学结合在一起的细节尚不很好地理解：一个想法是，时空不是基本概念，而是时空及其动态（即引力）可能会从某些显微镜中浮出水面自由度的方式类似于从大量水分子的集体行为中出现水的流动。因此，总体相对性应该与时空相结合，从某些对象的量子机械模型比空间和时间本身更基本的量子机械模型。这种表述将是量子重力的最终理论。为了实现这一目标，我的工作通过字符串理论工具探索了新兴的几何形状及其特性。在此提案中，我概述了一项研究计划，汇集了量子重力研究的最新进展，例如全息，纠缠熵，非交流性几何学和矩阵模型。这里的中心主题是非亚伯对象：x次y与y times x不同的数学实体，其中最简单的示例是方形矩阵。这样的非亚伯式实体以弦理论作为称为d-branes的基本对象的坐标，为我们提供了针对时空真实本质的线索。解开这些线索是我工作的主要目的。