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。例如，SM没有解释引力，并且将这种力纳入量子场论（QFT）的框架中特别困难，量子场论是粒子物理学的通用语言。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。因此，根据现代物理学的精神，我们很自然地得出结论，SM是一个“有效理论”，它只在一定的能量范围内有效，在这之后，它必须被一个更完整的理论，如弦理论所取代。伦敦玛丽皇后大学理论物理中心（CTP）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，CTP已经发现并开发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，即使在强大的计算机上也无法在合理的时间内完成。CTP开创的技术是计算这些振幅的捷径，它避免了传统方法的复杂性，并为连接不同理论振幅的令人惊讶的结构提供了新的启示。出乎意料的是，这些新的计算技术可以应用于粒子物理学领域之外的问题，例如研究双黑洞系统。CTP通过开发总体框架和提高显式应用中结果的精度，为最近的发展做出了贡献。寻找更好的方法来计算散射振幅仍然是一个重要的问题，因为这些方法将有助于充分理解LHC的结果，并模拟最近由LIGO和Virgo合作发现的引力波。弦理论为量子场论提供了意想不到的见解，例如引力和非引力理论之间的全息对偶，有可能提供新的方法来理解QFT在具有挑战性的制度。CTP继续其在全息术中的主导作用，用代数方法阐明其机制，计算将共形场论与反德西特空间联系起来的新矩阵，以及可积分段弦的发展。它最近在QFT方面的成果，例如量子码和CFT算子，伽罗瓦变换和图代数上的量子力学，正在融合，为复杂性和量子信息在弦理论中的作用提供新的视角和研究方向。这是弦理论和人工智能之间新对话的一部分，机器学习方法正在应用于QFT和弦，而新矩阵模型的弦数学正在为数据科学提供工具。CTP将建立在其领导地位，在扩展几何和非微扰方法M理论以及QFT。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. For instance, the SM does not account for gravity and it is particularly difficult to include this force in the framework of quantum field theory (QFT) which is the universal language of particle physics. 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 such as string theory. Research at the Centre for Theoretical Physics (CTP) 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 CTP has found and developed novel techniques for calculating scattering amplitudes. These are necessary because the usual calculus of Feynman diagrams becomes quickly intractable, and cannot be done in a reasonable amount of time even on powerful computers. The techniques pioneered by the CTP are shortcuts for calculating these amplitudes which evade the complications of traditional methods and shed new light on surprising structures that allow to connect amplitudes of different theories. Unexpectedly these new computational techniques can be applied to problems outside the particle physics domain, such as the study of binary black-hole systems. The CTP has contributed to this recent development both by developing the general framework and by improving on the precision of the results in explicit applications. Finding better methods for calculating scattering amplitudes remains an important problem, since these will be of use to fully understand LHC results and to model gravitational waves recently discovered by the LIGO and Virgo collaborations.String theory offers unexpected insights into quantum field theories, such as holographic dualities between gravitational and non-gravitational theories, with the potential to provide novel ways to understand QFTs in challenging regimes. The CTP has continued its leading role in holography, with algebraic approaches that illuminate its mechanisms, computations of new correlators linking conformal field theory to anti de Sitter space, and the development of integrable segmented strings. Its recent results in QFT, e.g. on quantum codes and CFT operators, Galois transformations and quantum mechanics on graph algebras, are converging to provide novel perspectives and research directions on the role complexity and quantum information have in string theory. This is forming part of new dialogues between string theory and artificial intelligence, where machine learning methods are being applied to QFT and strings, while the stringy mathematics of new matrix models is providing tools for data sciences. The CTP will build on its leadership in extended geometry and non-perturbative approaches to M-theory as well as QFT. 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.