Quantum Symmetries in String Theory

弦理论中的量子对称性

基本信息

批准号：
MR/T018909/1
负责人：
Benjamin Hoare
金额：
$ 121.18万
依托单位：
Durham University
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2020
资助国家：
英国
起止时间：
2020 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=MR%2FT018909%2F1
关键词：
Quantum Symmetries String Theory

项目摘要

If two people on opposite sides of the planet both drop a ball the same thing happens: the ball falls towards the ground with constant acceleration. This is a simple consequence of the rotational symmetry of the Earth's gravity. More generally, the power of symmetry lies in its ability to tell us that the laws of physics are related in situations that may look very different. In this way symmetry has had a profound impact on physics, often making impossible problems possible. The aim of my research is to develop novel symmetry-based methods tackling challenging open problems in theoretical physics.In the early 20th century two of the most successful theories of modern physics were discovered. The first, general relativity, describes classical gravity at large distances, while the second, quantum mechanics, underlies atomic-scale physics. However, attempting to unify them using standard methods leads to uncontrollable infinities. This long-standing problem suggests that a new framework is needed to develop a quantum theory of gravity.Starting from the elementary idea of considering fundamental objects that are extended in space, string theory has become a leading candidate for the quantum theory of gravity. Gravitons, the particles that carry the gravitational force, are oscillating closed loops of string. One of the most well-known facts about string theory is that it requires 10 space-time dimensions. Attempts to recover the 4 dimensions of our universe have been remarkably fruitful, leading to a wealth of new mathematics and fundamentally changing how we think about physical theories.One way to relate string theory to physics in 4 dimensions is through the AdS/CFT correspondence. This correspondence is a remarkable duality between two models. The first is a quantum theory of gravity described by closed strings on a highly symmetric curved space-time. The second is a quantum field theory in 4 dimensions, which has important connections to quantum chromodynamics: the gauge theory of the strong interaction holding protons and neutrons together in the nuclei of atoms.The power of the duality is that analytic computations in string theory give us new information about the strongly-coupled regime of quantum field theory. Strongly-coupled systems are typically hard to study and underlie many important open questions in science. Indeed, rigorously establishing the existence of a mass gap in Yang-Mills theory is one of the seven Millennium Prize problems. The AdS/CFT correspondence therefore ties together two long-standing problems of theoretical physics: describing a quantum theory of gravity and solving strongly-coupled quantum field theories.The strings of the AdS/CFT correspondence are not just moving on a curved space-time, but also in background fields. This can be compared to an electron moving in a background magnetic field: the electron interacts with the magnetic field causing it to follow a curved path. Many important string theories are of this type and they are typically difficult to study. Symmetry can provide us with a solution. One of the most striking manifestations of symmetry is integrability, a rich mathematical property of certain physical models. Integrability can be thought of as the presence of a large hidden symmetry that can be used to derive exact results. In special cases the strings of the AdS/CFT correspondence have this remarkable property and using the associated methods these theories can potentially be solved.The aim of my research is to develop novel symmetry-based methods advancing our knowledge of the role integrability plays in string theory and the AdS/CFT correspondence. This would allow us to solve string theories on non-trivial backgrounds and to construct new examples of gauge/gravity duality, thereby providing new insights into the fundamental nature of quantum gravity and strongly-coupled physics in the real world.

如果地球两侧的两个人都丢了一个球，就会发生同样的事情：球以恒定的加速度落向地面。这是地球引力旋转对称性的简单结果。更一般地说，对称性的力量在于它能够告诉我们物理定律在看起来可能非常不同的情况下是相关的。通过这种方式，对称性对物理学产生了深远的影响，常常使不可能的问题成为可能。我的研究目的是开发基于对称性的新颖方法来解决理论物理学中具有挑战性的开放问题。 20 世纪初，发现了现代物理学中两个最成功的理论。第一个是广义相对论，描述了远距离的经典引力，而第二个是量子力学，是原子尺度物理学的基础。然而，尝试使用标准方法统一它们会导致无法控制的无穷大。这个长期存在的问题表明需要一个新的框架来发展量子引力理论。从考虑空间中延伸的基本物体的基本思想出发，弦理论已成为量子引力理论的主要候选者。引力子是携带引力的粒子，正在振荡闭合的弦环。关于弦理论最著名的事实之一是它需要 10 个时空维度。恢复宇宙 4 维的尝试已经取得了显着的成果，带来了大量的新数学，并从根本上改变了我们对物理理论的思考方式。将弦理论与 4 维物理联系起来的一种方法是通过 AdS/CFT 对应关系。这种对应关系是两个模型之间显着的二元性。第一个是用高度对称弯曲时空上的闭合弦描述的量子引力理论。第二个是 4 维量子场论，它与量子色动力学有重要联系：原子核中将质子和中子保持在一起的强相互作用的规范理论。对偶性的力量在于弦理论中的解析计算给出我们获得了有关量子场论强耦合机制的新信息。强耦合系统通常很难研究，并且是科学中许多重要的开放问题的基础。事实上，在杨-米尔斯理论中严格证明质量间隙的存在是七个千年奖问题之一。因此，AdS/CFT 对应关系将两个长期存在的理论物理问题联系在一起：描述量子引力理论和求解强耦合量子场论。AdS/CFT 对应关系的弦不仅仅是在弯曲时空上移动，而且也在背景字段中。这可以与在背景磁场中移动的电子进行比较：电子与磁场相互作用，使其沿着弯曲的路径移动。许多重要的弦理论都属于这种类型，并且它们通常很难研究。对称性可以为我们提供解决方案。对称性最引人注目的表现之一是可积性，这是某些物理模型的丰富数学属性。可积性可以被认为是存在一个大的隐藏对称性，可以用来导出精确的结果。在特殊情况下，AdS/CFT 对应的字符串具有这种显着的属性，并且使用相关的方法可以潜在地解决这些理论。我的研究目的是开发新颖的基于对称性的方法，以增进我们对可积性在字符串中所扮演的角色的了解。理论和 AdS/CFT 对应关系。这将使我们能够在非平凡的背景下解决弦理论，并构建规范/引力对偶性的新例子，从而为现实世界中量子引力和强耦合物理的基本性质提供新的见解。