Supergravity, quantum field theory and black holes

理论物理学的两个基石是量子理论和引力理论，即爱因斯坦的广义相对论。量子力学的本质是粒子有时表现得像波，反之亦然。四种已知力中的三种本质上是量子力学的。它们是电磁力、弱核力和强核力。事实上，这些力是由粒子物理学的标准模型描述的。这是一种量子场论，更准确地说是量子杨-米尔斯理论，它现在已经在粒子加速器中得到了非常精确的检验。另一方面，第四种力，引力，由广义相对论描述。它说，比如说，一个苹果落在艾萨克·牛顿的头上，是时空弯曲的一种表现。为了更好地理解这种感觉，想象一下一个巨大的乳胶橡胶板，中间放着一个铅球，把它拉下来。如果我们现在把一个弹珠放在床单上，它会像被某种力拉着一样向铅球滚去。广义相对论也非常精确，已经用许多不同的方法进行了检验。这个理论最有趣的方面之一是它预言了黑洞的存在。在黑洞中，引力是如此之强，也就是说，时空的曲率是如此之大，以至于连光也无法逃脱。我们现在认为所有星系的中心都有一个巨大的黑色。广义相对论也是我们关于宇宙起源的理论的基础，即一切都在大约100亿年前开始于一个非常微小的压缩状态，然后爆炸-大爆炸。所以，我们有两个美丽的理论，标准模型和广义相对论，两者都非常准确。但它们在数学上是不相容的！这怎么可能？关键在于，这两种理论所涉及的尺度非常不同：在小尺度上，对于当前的粒子物理学来说，引力是如此之弱，以至于我们可以忘记它;同样，当所有其他粒子力都可以忽略不计时，广义相对论也适用于非常大的尺度。这就是为什么我们可以让这两个不相容的理论愉快地共存。然而，我们知道，在某些情况下，我们需要这两个理论：例如在黑洞内部和大爆炸。将两者统一起来的理论称为量子引力理论。我在研究一个叫做弦理论的候选量子引力。弦理论的主要思想是，一切都是由非常小的弦环或弦段组成的。这些弦的振动，就像小提琴上的不同音符，通过量子力学，每一个都将成为不同的基本粒子。如果弦以一种方式振荡，它就是电子，如果以另一种方式振荡，它就是质子，等等。理解这到底是如何发生的数学是我的工作。有趣的是，弦理论与非常有趣的数学有关，特别是几何学，而这两者之间的相互作用对我的工作是一个很大的启发。对称性一直是构建标准模型和通用模型的主要指导原则。相对论我们所知道的每一个粒子不是玻色子就是费米子。玻色子，例如光子，与力有关，而费米子，例如电子，与物质有关。一种非常有趣的对称性，称为超对称性，本质上是通过对称性将玻色子与费米子联系起来的唯一方法。它是弦论的核心组成部分，基于大量的提示，我认为对弦论中的超对称性有更深的数学理解将导致对弦论本身有更深的理解。这就是我打算做的工作，我希望它能在确定弦理论是否能描述自然的旅程中迈出重要的一步。

The two cornerstones of theoretical physics are quantum theory and our theory of gravity, Einstein's theory of General Relativity.The essence of quantum mechanics is that particles sometimes behave like waves and vice-versa. Three of the four known forces are quantum mechanical in nature. These are the electromagnetic, the weak nuclear and the strong nuclear forces. Indeed these force are described by the Standard Model of particle physics. This is a quantum field theory, more precisely a quantum Yang-Mills theory, and it has now been tested to extraordinary precision in particle accelerators.The fourth force, gravity, on the other hand hand, is described by General Relativity. It says that the phenomenon of, say, an apple falling onto Isaac Newton's head, is a manifestation of the curvature of space-time. To get a flavour of this, imagine a big latex rubber sheet with a shot-put sitting in the middle stretching it down. If we now put a marble on the sheet, it will roll toward the shot-put as if it is being pulled by some force.General Relativity is also very accurate, having been tested in many different ways. One of the most interesting aspects of the theory is that it predicts the existence of black holes. In a black hole gravity is so strong, that is, the curvature of spacetime is so great, that even light cannot escape. We now think that all galaxies have a huge black sitting at their centre. General Relativity is also the basis for our theory of the origin of the universe, that everything began about 10 billion years ago in a very tiny compressed state and then exploded - the Big Bang .So, we have two beautiful theories, the Standard Model and General Relativity, and both are very accurate. But they are mathematically incompatible! How can this possibly be? The point is that the two theories are associated with very different scales: on small scales, for current particle physics, gravity is so weak that we can just forget about it. Similarly, General Relativity is applicable on very large scales when all other particle forces are negligible. This is why we can have the two incompatible theories happily co-existing.However, we know that there are some situations where we need both theories: for example inside black holes and at the Big Bang. A theory that unifies the two is called a theory of quantum gravity. I work on a candidate quantum gravity called string theory. The main idea of string theory is that everything is really made up of very tiny little loops or segments of string. The oscillations of these strings, like the different notes on a violin, would each become, via quantum mechanics, a different elementary particle. If the string oscillates one way it's an electron, if it oscillates another way it's a proton and so on. Understanding the mathematics of exactly how this might happen is something that I work on. Interestingly, string theory is associated with very interesting mathematics, particularly geometry, and the interplay between the two is a great inspiration in my work.Symmetry has been a major guiding principle in constructing both the Standard Model and General Relativity. Now, every particle that we know of is either a boson or a fermion. The bosons, a photon for example, are associated with forces, while the fermions, an electron for example, are associated with matter. A very interesting symmetry, called supersymmetry, is essentially the only way to connect bosons with fermions via a symmetry. It is a central component of string theory and, based on a lot of hints, I think obtaining a deeper mathematical understanding of supersymmetry in string theory will lead to a deeper understanding of string theory itself. This is what I am proposing to work on and I hope that it will provide a significant step on the journey to determine whether or not Nature is described by string theory.