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物质通过特定力相互作用的假设，在最小的尺度上都表现得像点状粒子。这些成功在粒子物理学的“标准模型”（SM）中得到了简洁的总结，自从在大型强子对撞机（LHC）上发现希格斯粒子以来，我们很容易认为它是对宇宙最小尺度的完整描述。然而，事实并非如此。例如，SM并没有解释引力，而且在量子场论（QFT）的框架中包含这种力是特别困难的，而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量子场效应和引力。在许多现代物理学的精神中，因此很自然地得出这样的结论：SM是一种“有效理论”，它只在某种能量尺度下有效，在此之后，它必须被更完整的理论（如弦理论）所取代。伦敦玛丽女王大学理论物理中心（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，既处理QFT问题，也处理弦理论问题。在QFT方面，CTP发现并发展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就变得难以处理，即使在功能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，它避开了传统方法的复杂性，并揭示了令人惊讶的结构，这些结构允许将不同理论的振幅联系起来。出乎意料的是，这些新的计算技术可以应用于粒子物理领域以外的问题，比如对双黑洞系统的研究。CTP通过开发一般框架和提高显式应用程序中结果的精度，对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，因为这些方法将用于充分理解LHC的结果，并模拟LIGO和Virgo合作最近发现的引力波。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二象性，有可能为理解具有挑战性的体系中的量子场效应提供新的方法。CTP继续在全息学中发挥着主导作用，用代数方法阐明了其机制，计算了将共形场理论与反德西特空间联系起来的新相关器，以及可积分段弦的发展。其在量子傅立叶变换中的最新研究成果，如关于量子码和CFT算子的研究成果、关于图代数的伽罗瓦变换和量子力学的研究成果，正在不断融合，为复杂性和量子信息在弦理论中的作用提供了新的视角和研究方向。这是弦理论与人工智能之间新对话的一部分，机器学习方法正被应用于QFT和字符串，而新矩阵模型的弦数学正在为数据科学提供工具。CTP将建立在其在扩展几何和m理论以及QFT的非微扰方法方面的领导地位。上述许多主题都属于使用弦理论作为工具来理解QFT和粒子物理中的难题的分类。即使弦理论被证明不是SM的正确短距离补全，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.