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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.

这个项目涉及弦理论和量子场论（QFT）。有两大目标。第一部分是使用弦理论的工具来描述QFT的其他棘手的制度。第二部分是在弦理论中使用新的几何工具来描述引力和我们可观测的宇宙。QFT非常好地描述了我们宇宙亚原子水平上的相互作用，支持所有实验验证的粒子和相互作用。QFT方程，除非在特殊情况下，是笨重的，不适合直接分析。标准的方法是用一种称为微扰理论的方法来近似方程。这要求粒子之间的相互作用很弱，而不是普遍的情况。通常，相互作用很强，这种情况称为强耦合，微扰理论近似失效。这个问题是理解粒子物理学许多方面的主要限制。此外，QFT并不描述宏观相互作用，特别是引力。如果我们处理的是非常致密的物体，比如黑洞，那么我们需要找到一个结合爱因斯坦广义相对论和QFT的理论。最有可能做到这一点的是弦理论。为了工作，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之外，还必须存在六个额外的维度，它们的几何形状非常小，因此在今天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，它有一个额外的圆形方向。描述可观测宇宙的物理学成为一个与特定空间的几何学紧密相关的问题，相反，弦理论的输出要求可感知的物理学导致新的几何技术。这样，我们就可以理解量子修正来自弦理论本身。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。全息术是两种理论之间的等价物，让我们称它们为理论A和理论B。理论A是一个d+1维引力理论，而理论B是在平坦的（没有引力）d维空间中的QFT。全息术意味着理论A可以用来了解理论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解的，关于强耦合机制的信息完全由对称性决定。全息术意味着我们可以确定理论A（引力理论）的性质（也许是模糊的）。相反，通过经典引力，理论A可以用来描述理论B中的强耦合机制。即使理论A和理论B都不是现实的模型--人们通常会对对偶性进行简化假设--人们也可能希望由此产生的特征是普遍的，从而在粒子物理学的其他困难问题上给我们一些新的教训。第一部分的建议是关于发展全息在一个新的范例，以及使用可积性来探索QFT的属性。接下来，在引力的背景下，在理解黑洞方面出现了新的想法。从弦论衍生出来的对称性，例如超对称性，已经导致了获得新类型黑洞的新技术，以及理解它们的几何和物理性质。许多有趣的问题出现了：量子修正对这些黑洞解的作用是什么？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的唯象模型？这样做需要理解空间的几何学。什么样的几何形状可以形成我们宇宙的真实模型？量子修正的作用是什么？这些是构成本建议第二部分的各类问题。