Stongly Coupled Field Theories, String Theory and Gravity

强耦合场论、弦理论和引力

基本信息

批准号：
ST/P000487/1
负责人：
Jan Gutowski
金额：
$ 2.72万
依托单位：
University of Surrey
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2017
资助国家：
英国
起止时间：
2017 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=ST%2FP000487%2F1
关键词：
Stongly Coupled Field Theories String

项目摘要

This project is concerned with string theory and quantum field theory (QFT). There are two broad aims. Part I is to use tools inspired from string theory to describe otherwise intractable regimes of QFT. Part II is to use new geometric tools within string theory to describe aspects of gravity and our observable universe. QFT describes interactions at the sub-atomic level of our universe exceptionally well, underpinning all experimentally verified particles and interactions. The equations of QFT, except in special circumstances are unwieldy and not amenable to a direct analysis. The standard approach is to approximate the equations in a manner known as perturbation theory. This requires the interactions between particles be weak, not a universal situation. Often, the interactions are strong, a situation known as strong coupling, and the perturbation theory approximation breaks down. This problem is a major limitation for understanding many aspects of particle physics. Moreover, QFT does not describe macroscopic interactions, in particular gravity. If we are dealing with very dense objects such as black holes, then we need to find a theory that incorporates Einstein's theory of general relativity and QFT. The leading candidate that does this is string theory. In order to work, it requires stringent mathematical conditions be imposed. For example, in addition to the three dimensions we observe, there must exist six additional dimensions, whose geometry is very small and so not visible to present day experiment. A rough analogy is with a hose: from a distance it looks one-dimensional, but on closer inspection there is an additional circular direction. Describing the physics of the observable universe becomes a problem closely tied to the geometry of certain spaces, and conversely, demanding sensible physics as an output of string theory leads to new geometric techniques. One can then understand quantum corrections as coming from the string theory itself. String theory has led to new ideas in our understanding of QFT and gravity. We start with a strongly coupled QFT. Holography is an equivalence between two theories, let us call them theory A and theory B. Theory A is a d+1-dimensional gravity theory while theory B is QFT in flat (without gravity) d-dimensional space. Holography means that theory A can be utilised to learn about strong coupling aspects of theory B and vice versa. For example, theory B can be integrable, meaning it is completely soluble, and information about the strong coupling regime is determined purely by symmetry. Holography means we can determine (perhaps obscure) properties of theory A, the gravity theory. Conversely, via classical gravity, theory A can be used to describe regimes of strong coupling in theory B. Even if theory A nor theory B are not realistic models - one typically makes simplifying assumptions for the dualities to work -- one might hope the resulting features are universal, teaching us some new lessons on otherwise difficult problems in particle physics. Part I of this proposal is concerned with developing holography in a new paradigm of examples, as well as using integrability to explore properties of QFT. Next, in the context of gravity, new ideas have arisen in understanding black holes. Symmetries that derive from string theory, e.g. supersymmetry, have led to novel techniques for obtaining new types of black holes, as well as understanding their geometric and physical properties. Many interesting questions arise: what is the role of quantum corrections to these black hole solutions? Are they stable? A different but related question is how can we use string theory to describe quasi-realistic phenomenological models? Doing so requires understanding the geometry of spaces. What types of geometries lead to realistic models of our universe? What is the role of quantum corrections? These are the types of questions that form part II of this proposal.

该项目涉及弦理论和量子场论（QFT）。有两个广泛的目标。第一部分是使用受弦理论启发的工具来描述其他棘手的 QFT 机制。第二部分是使用弦理论中的新几何工具来描述重力和我们可观测宇宙的各个方面。 QFT 非常好地描述了宇宙亚原子层面的相互作用，为所有经过实验验证的粒子和相互作用提供了基础。除特殊情况外，QFT 方程都很笨重且不适合直接分析。标准方法是以微扰理论的方式近似方程。这要求粒子之间的相互作用很弱，不是普遍情况。通常，相互作用很强，这种情况称为强耦合，并且微扰理论近似会失效。这个问题是理解粒子物理学许多方面的主要限制。此外，QFT 不描述宏观相互作用，特别是重力。如果我们处理的是黑洞等非常致密的物体，那么我们需要找到一种结合爱因斯坦广义相对论和 QFT 的理论。做到这一点的主要候选者是弦理论。为了发挥作用，它需要施加严格的数学条件。例如，除了我们观察到的三个维度外，还必须存在六个附加维度，其几何形状非常小，因此在当今的实验中是不可见的。一个粗略的类比是软管：从远处看，它看起来是一维的，但仔细观察时，会发现有一个额外的圆形方向。描述可观测宇宙的物理现象成为一个与某些空间的几何学密切相关的问题，相反，要求敏感物理作为弦理论的输出会导致新的几何技术。然后，人们可以将量子校正理解为来自弦理论本身。弦理论为我们理解 QFT 和引力带来了新的想法。我们从强耦合 QFT 开始。全息术是两种理论的等价，我们称之为理论A和理论B。理论A是d+1维引力理论，而理论B是平坦（无引力）d维空间中的QFT。全息意味着理论 A 可用于了解理论 B 的强耦合方面，反之亦然。例如，理论 B 可以是可积的，这意味着它是完全可溶的，并且有关强耦合机制的信息纯粹由对称性决定。全息术意味着我们可以确定（也许是模糊的）理论 A（引力理论）的属性。相反，通过经典引力，理论 A 可以用来描述理论 B 中的强耦合状态。即使理论 A 和理论 B 都不是现实的模型——人们通常会为二元性的工作做出简化的假设——人们可能希望得到结果特征是普遍的，给我们一些关于粒子物理学中其他困难问题的新教训。该提案的第一部分涉及在新的示例范式中开发全息术，以及利用可积性来探索 QFT 的属性。接下来，在引力的背景下，出现了理解黑洞的新想法。来自弦理论的对称性，例如超对称性带来了获得新型黑洞以及理解它们的几何和物理特性的新技术。出现了许多有趣的问题：量子修正对这些黑洞解决方案的作用是什么？他们稳定吗？一个不同但相关的问题是我们如何使用弦理论来描述准现实现象学模型？这样做需要了解空间的几何形状。哪些类型的几何形状可以产生真实的宇宙模型？量子修正的作用是什么？这些是构成本提案第二部分的问题类型。