String Theory, Gauge Theory and Duality

我们的宇宙是由粒子组成的，这一点常常被认为是理所当然的。近一百年来，我们已经有了越来越多的预测模型，这些模型基于这样的假设：在非常小的尺度上，物质的行为就像通过特定力相互作用的点粒子。这些力，以及它们所作用的粒子的性质，是粒子物理学的“标准模型”（SM）。自从在大型强子对撞机（LHC）上发现希格斯粒子以来，人们可能会认为SM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），粒子物理学的计算语言，被应用于引力理论时，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法修复的分歧。这是一个问题，因为任何试图描述黑洞或早期宇宙的理论都需要合理地将量子场论和引力联合收割机结合起来。从现代物理学的精神来看，我们可以合理地猜测，SM理论只适用于某一能量尺度，在此之后，它必须被一个更完整的理论所取代。弦论是这一理论的主要候选者，它认为物质不是由点粒子组成的，而是由一维的弦组成的（很明显，这个理论也有更高维的物体，称为"膜"）。虽然这解决了将重力与SM相结合的问题，但它也提出了新的挑战，例如额外空间维度的存在。如果要认真对待弦理论，就必须理解如何解释这些预言，伦敦大学玛丽皇后分校的弦理论研究中心（CRST）在理解弦理论及其对QFT的影响方面发挥了重要作用。该小组目前的重点是广泛的，处理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复杂，即使在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。找到更好的计算技术仍然是一个重要的问题，因为这些结果将有助于充分理解LHC的结果。前一段中的许多理论都是在弦理论的背景下出现的，而且往往可以在膜上出现。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。这是必要的，因为这样的理论往往没有膨胀参数。CRST一直站在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，例如算子的尺度。然而，这些技术只在一小部分理论中得到了应用，为更广泛的理论开发这样的工具仍然是一个紧迫的问题。CRST在理解弦理论方面也取得了重大进展。弦论中出现的几何展现了令人惊讶的新对偶，它们与非常不同的数学空间相关。弦理论家对这些对偶性的研究很感兴趣，因为这个领域仍然缺乏对弦几何空间的完整理解。上述许多主题都属于使用弦理论作为理解QFT和粒子物理学难题的工具的范畴。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。

That our universe is made out of particles is often taken for granted. For nearly a hundred years, we have had increasingly predictive models based on the assumption that, at very small scales, matter behaves as point particles which interact via specific forces. These forces, as well as the nature of the particles upon which they act, are the "Standard Model" (SM) of particle physics. Since the discovery of the Higgs at the Large Hadron Collider (LHC), it is perhaps tempting to consider the SM 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 calculational language of particle physics, is applied to theories with gravity, the results are disastrous. In particular, many calculations done in this framework lead to unfixable divergences. This is a problem, since any theory attempting to describe black holes or the early universe will need to sensibly combine both QFT and gravity. In the spirit of much of modern physics, it is thus reasonable to guess that the SM only works 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 (as has become clear, this theory also has higher-dimensional objects called "branes"). Although this solves the problem of combining 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.The Centre for Research in String Theory (CRST) at Queen Mary University of London has been instrumental in understanding string theory and its consequences for QFT. The current focus 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 complicated quickly, and can not be done in a reasonable amount of time even on a computer. The techniques pioneered by the CRST are shortcuts for calculating these amplitudes which evade the complications of traditional methods. Finding better techniques for such calculations remains an important problem, since these results will be of use to fully understand LHC results.Many of the theories in the previous paragraph occur within the context of string theory, and can often arise on branes. 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 necessary 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 the quantities of interest, e.g. scaling dimensions of operators. These techniques are known for only a small subset of theories, however, and developing such tools for broader classes of theories remains a pressing problem.The CRST has also made significant progress in understanding string theory in its own right. Geometries that appear in string theory exhibit surprising new dualities that relate very different mathematical spaces. The study of these dualities is of interest to string theorists, since the field still lacks a complete understanding of the space of stringy geometries.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.