Amplitudes, Strings and Duality

人们普遍认为，粒子是我们宇宙的基本组成部分。几十年来，越来越多的预测模型是基于这样的假设开发的：通过特定力相互作用的物质，在最小尺度上表现得像点状粒子。粒子物理学的“标准模型”（SM）简洁地概括了这些成就。自从在大型强子对撞机（LHC）上发现希格斯玻色子以来，我们很想把它看作是对宇宙最小尺度的完整描述，但事实并非如此。特别是，SM没有考虑重力。当量子场论（QFT），粒子物理学的通用语言，被应用到引力，结果是灾难性的。特别是，在这个框架中进行的许多计算导致无意义的无穷大。这是一个重大的挑战，因为任何试图描述黑洞或早期宇宙的理论都必须能够统一QFT和引力。从现代物理学的精神来看，我们可以很自然地得出结论：SM是一个“有效理论”，它只在一定的能量尺度下才有效，在此之后，它必须被一个更完整的理论所取代。这个基础理论的主要候选者是弦论，它提出物质不是由点粒子组成的，而是一维的弦，甚至是更高维的被称为“膜”的物体。虽然这解决了统一重力与SM的问题，但它也提出了新的挑战，例如额外空间维度的存在。如果弦理论要得到认真对待，了解如何解释这些预测是必要的。伦敦玛丽女王大学的弦理论研究中心（CRST）的研究重点是理解QFT、弦理论及其相互联系。该小组的活动范围很广，涉及QFT和弦理论的问题。在QFT方面，CRST发现了计算散射振幅的新技术。这些是必要的，因为通常的费曼图演算很快变得棘手，即使在功能强大的计算机上也无法在合理的时间内完成。CRST开创的技术是计算这些振幅的捷径，避免了传统方法的复杂性。寻找更好的方法来进行这样的计算仍然是一个重要的问题，因为这些方法将有助于完全理解LHC的结果或模拟LIGO最近发现的引力波。上面提到的许多理论都可以在弦理论的背景下实现。虽然这样的理论很复杂，但可以同时使用场论和弦论技术来得到不依赖微扰技术的结果。这是至关重要的，因为这样的理论往往没有膨胀参数。CRST一直处于理解这些理论的最前沿，并开发了计算感兴趣的量的新工具，例如标度维数，指数和配分函数。然而，这些技术只适用于一小部分理论，为更广泛的理论类别开发工具仍然是一个紧迫的问题。CRST对理解弦论中的全息对偶性做出了重大贡献，将引力理论与非引力理论联系起来，同时与混沌和量子信息建立了新的联系，开辟了新的研究方向。它导致了一系列丰富的几何学和场论的推广研究，目前的焦点是特殊的场论及其对M理论结构的影响。上述许多主题都属于使用弦理论作为工具来理解QFT和粒子物理学中的困难问题的类别。即使弦理论不是SM的正确短程完备化，它作为解决QFT问题的工具也是安全的。

It is widely believed that particles are the fundamental building blocks of our universe. Over many decades increasingly predictive models were developed based on the assumption that matter, which interacts via specific forces, behaves like pointlike particles down to the tiniest scales. These successes are neatly summarised in the "Standard Model" (SM) of particle physics, and since the discovery of the Higgs at the Large Hadron Collider (LHC), we are tempted to consider it to be a complete description of the universe at its smallest scales.However, this is not the case. In particular, the SM does not account for gravity. When quantum field theory (QFT), the universal language of particle physics, is applied to gravity, the results are disastrous. In particular, many calculations done in this framework lead to meaningless infinities. This poses a major challenge, since any theory attempting to describe black holes or the early universe must be able to unify QFT and gravity. In the spirit of much of modern physics, it is thus natural to conclude that the SM is an "effective theory" which is only valid up to some energy scale, after which it must be replaced by a more complete theory.The leading candidate for this underlying theory is String Theory, which proposes that matter is not made of point particles, but one-dimensional strings and even higher-dimensional objects called "branes". Although this solves the problem of unifying gravity with the SM, it also presents new challenges, such as the existence of extra spatial dimensions. Understanding how to interpret these predictions is necessary if string theory is to be taken seriously. Research at the Centre for Research in String Theory (CRST) at Queen Mary University of London focuses on understanding QFT, string theory and their interconnections. The range of activities of the group is broad, dealing with issues in both QFT and string theory alike. On the QFT side, the CRST has found novel techniques for calculating scattering amplitudes. These are necessary because the usual calculus of Feynman diagrams becomes quickly intractable, and can not be done in a reasonable amount of time even on powerful computers. The techniques pioneered by the CRST are shortcuts for calculating these amplitudes which evade the complications of traditional methods. Finding better methods for such calculations remains an important problem, since these will be of use to fully understand LHC results or to model gravitational waves recently discovered by LIGO.Many of the theories mentioned above can be realised within the context of string theory. Although such theories are complicated, it is possible to use both field and string theory techniques to get results that do not rely on perturbative techniques. This is crucial because such theories often do not have expansion parameters. The CRST has been at the forefront of understanding such theories, and has developed new tools for calculating quantities of interest, e.g. scaling dimensions, indices, and partition functions. These techniques are known for only a small subset of theories, however, and developing tools for broader classes of theories remains a pressing problem. The CRST has made significant contributions to the understanding of holographic dualities in string theory, relating gravitational to non-gravitational theories, while making new connections to chaos and quantum information, which have opened up novel research directions. It has led the study of a rich array of generalizations of geometry and field theory, a present focus being exceptional field theories and their implications for the structure of M-theory. Many of the above topics fall under the classification of using string theory as a tool for understanding difficult problems in QFT and particle physics. Even if string theory turns out not to be the correct short-distance completion of the SM, its use as a tool for solving problems in QFT is secure.