Fundamental Implications of Fields, Strings and Gravity

牛顿物理学很好地描述了我们的宇宙，只要感兴趣的物体不是太小，不是移动太快，或者不是太密集。在很小的尺度上，牛顿物理学被量子物理学所取代。此外，如果相互作用的速度接近光速，那么量子物理学就会被量子场论(QFT)所取代。这一理论是科学发现的里程碑，支持所有经过实验验证的粒子和相互作用。QFT的标准方法依赖于微扰理论，该理论假设所有的相互作用都是弱的。在许多情况下情况并非如此，由此产生的理论被认为是强耦合的。在粒子物理标准模型背后的理论中，相互作用通常并不弱。这使我们无法解释夸克禁闭等现象，从而形成构成物质的质子和中子。这是一个概念上的问题，也是现象学应用的一个主要限制。如果我们处理的是极其密集的物体呢？例如，如果地球内部的所有物质都被压缩到一个半径为几毫米的球体中，那么上述理论就会崩溃。在这种情况下，人们需要将爱因斯坦的广义相对论与量子场论结合起来。然而，没有完全一致的方法来做到这一点，这给我们对宇宙的理解留下了一个巨大的漏洞。唯一成功地将量子力学和广义相对论结合在一起的理论是弦理论。该理论的自洽要求施加严格的数学条件。例如，除了我们习惯的三个空间维度之外，还必须存在额外的六个空间维度。为了解决这个问题，人们必须“压缩”，即假设额外的维度跨越卷曲的几何图形，这在目前的实验中是看不见的。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。描述可见宇宙的物理成为一个与某些空间的几何密切相关的问题。值得注意的是，弦理论导致了关于描述强耦合QFT的新想法。其中一种被称为全息术的工具代表了这样一种想法，即我们的时空对更高维度的信息进行编码，就像全息图是三维图像的二维表示一样。结果表明，四维强耦合QFT与弱耦合五维引力理论有关，在该理论中，我们可以应用微扰技术进行计算。在过去的十年里，这一想法在理论物理学方面带来了许多令人兴奋的新发展。它还被用来理解在极端压力和温度条件下(夸克胶子等离子体)获得的实验结果。这个项目的目标有两个：使用弦理论的这些新工具来理解量子力学中的强耦合机制；以及使用弦理论来模拟今天观察到的四维时空。例如，弦理论中的许多思想和概念已经极大地改变了我们对强耦合QFT的看法。还有一些强耦合QFT的新例子，在这些例子中，计算变得很容易处理。虽然不是真实的模型，但它们与现实世界有许多共同的定性特征，否则很难理解。通过研究这些新的例子，我们希望阐明在实验感兴趣的理论中，像限制这样的模糊机制是如何起作用的。通过利用量子场论中的这些发展，我们希望揭示重现描述现代粒子物理的弦紧凑化所需的确切条件。

Newtonian physics describes our universe well, provided the objects of interest are not too small, do not move too fast, or are not too dense. At a small length scales, Newtonian physics is replaced by quantum physics. In addition, if interactions involve speeds close to that of light, then quantum physics is replaced by quantum field theory (QFT). This theory is a milestone of scientific discovery and underpins all experimentally verified particles and interactions. The standard approach to QFT relies on perturbation theory, which assumes that all interactions are weak. There are many situations where that is not the case, and the resulting theory is said to be strongly coupled. In the theory underlying the standard model of particle physics the interactions are generally not weak. This prevents us from explaining phenomena such as the confinement of quarks to form the protons and neutrons that make up matter. This is a conceptual problem, and a major limitation for phenomenological applications.What about if we are dealing with extremely dense objects? For example, if all of the matter inside the Earth were compressed to fill a sphere with a radius of a few millimetres, then the above theories would break down. In this case, one would need to incorporate Einstein's theory of general relativity with quantum field theory. However, there is no completely consistent way to do this, leaving a gaping hole in our understanding of the universe. The only theory that successfully combines QFT with general relativity is string theory. Self-consistency of the theory demands stringent mathematical conditions be imposed. For example, there must exist six extra spatial dimensions in addition to the three spatial dimensions we are accustomed to. To resolve this, one must ``compactify'', i.e. posit that the extra dimensions span curled geometries, 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.Remarkably, string theory has led to new ideas concerning the description of strongly coupled QFTs. One such tool, known as holography, represents the idea that our space-time encodes information of a higher dimensional one, much like a hologram is a two-dimensional representation of a three-dimensional picture. It turns out that the strongly coupled QFT in four-dimensions relates to a weakly coupled five-dimensional gravity theory in which we may apply perturbative techniques to perform computations. Over the past decade, this idea has led to many new and exciting developments in theoretical physics. It has also been used to understand experimental results obtained under extreme pressure and temperature conditions (quark gluon plasma). The aims of this project are two-fold: to use these new tools from string theory to understand the strongly coupled regime of QFT; and to use string theory to model the four-dimensional space time observed today. For example, many of the ideas and concepts within string theory have drastically changed the way we think about strongly coupled QFTs. There are also new examples of strongly coupled QFTs, in which calculations have become tractable. Although not realistic models, they share with the real world many common qualitative features, which are otherwise hard to understand. By studying these new examples we hope to shed light on how obscure mechanisms such as confinement work in theories of experimental interest. By utilising these developments in quantum field theory we hope to undercover the exact conditions required to reproduce the string compactification that describes modern particle physics.