Supergravity, quantum field theory and black holes

理论物理的两个基石是量子理论和我们的引力理论，即爱因斯坦的广义相对论。量子力学的本质是，粒子有时表现为波，反之亦然。已知的四种力中有三种本质上是量子力学的。这就是电磁力、弱核力和强核力。事实上，这些力是由粒子物理的标准模型描述的。这是一种量子场论，更确切地说是量子杨-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测试。另一方面，广义相对论描述了第四种力--引力。它说，比方说，苹果掉到艾萨克·牛顿头上的现象，是时空弯曲的一种表现。要尝到这种味道，想象一下一张巨大的乳胶橡皮板，中间有一个铅球，把它向下拉。如果我们现在把一块大理石放在板子上，它会滚向铅球，就像是被某种力量拉着一样。广义相对论也是非常准确的，已经用许多不同的方式进行了检验。该理论最有趣的方面之一是它预测了黑洞的存在。在黑洞中，引力是如此强烈，也就是说，时空的曲率是如此之大，以至于连光都无法逃脱。我们现在认为，所有星系的中心都有一个巨大的黑色区域。广义相对论也是我们宇宙起源理论的基础，即一切都始于100亿年前一种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，这两个理论都非常准确。但它们在数学上是不相容的！这怎么可能呢？关键是，这两种理论与非常不同的尺度有关：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。类似地，当所有其他粒子力都可以忽略时，广义相对论适用于非常大的尺度。这就是为什么我们可以让两个不相容的理论幸福地共存。然而，我们知道在某些情况下，我们需要两个理论：例如在黑洞内和在大爆炸中。将两者统一起来的理论被称为量子引力理论。我正在研究一种叫做弦理论的候选量子引力。弦理论的主要思想是，一切实际上都是由非常微小的线环或线段组成的。这些弦的振荡，就像小提琴上的不同音符一样，通过量子力学，每一个都会变成不同的基本粒子。如果弦朝一个方向摆动，它就是电子，如果它朝另一个方向摆动，它就是质子，以此类推。我正在研究的是如何准确地理解这种情况发生的数学原理。有趣的是，弦理论与非常有趣的数学联系在一起，特别是几何，两者之间的相互作用是我工作中的巨大灵感。对称性一直是构建标准模型和广义相对论的主要指导原则。现在，我们所知道的每一个粒子要么是玻色子，要么是费米子。玻色子，例如一个光子，与力有关，而费米子，例如一个电子，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。它是弦理论的核心组成部分，基于大量的提示，我认为对弦理论中超对称性的更深入的数学理解将导致对弦理论本身的更深层次的理解。这就是我提议要做的工作，我希望它将在确定是否用弦理论来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.