String Theory, Gauge Theory and Duality

我们的宇宙是由粒子组成的这一观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，物质表现为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）。自从去年在大型强子对撞机（LHC）上发现希格斯粒子以来，人们可能很容易认为，SM是对宇宙最小尺度的完整描述。然而，事实并非如此。特别是，SM不考虑重力。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，在这个框架下进行的许多计算导致了无法解决的分歧。这是一个问题，因为任何关于早期宇宙的理论都需要将量子力学和引力合理地结合起来。在许多现代物理学的精神中，因此有理由猜测，SM只能达到某种能量尺度，在此之后，它就变成了一个更完整理论的糟糕近似。这个潜在理论的主要候选是弦理论，它提出物质不是由点粒子组成的，而是由一维弦组成的（很明显，这个理论也有被称为“膜”的高维物体）。虽然这解决了重力与SM结合的问题，但也带来了新的问题，比如额外空间维度的存在。如果要认真对待弦理论，了解如何解释这些预测是必要的。伦敦大学玛丽皇后学院的弦理论研究中心（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和弦理论中的问题。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，即使在计算机上也不能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。寻找更好的计算技术仍然是一个重要的问题，因为这些结果可能是理解大型强子对撞机结果所必需的。上一段中的许多理论都是在弦理论的背景下出现的，并且经常出现在膜上。虽然这样的理论很复杂，但可以同时使用场理论和弦理论技术来获得不依赖于摄动技术的结果。这是必要的，因为这类理论通常没有膨胀参数。CRST一直处于理解这些理论的前沿，并开发了计算感兴趣数量的新工具，例如缩放算子的维度。然而，这些技术只适用于一小部分理论，而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本身在理解弦理论方面也取得了重大进展。弦理论中出现的几何表现出令人惊讶的新对偶性，它们与非常不同的数学空间有关。弦理论家对这些对偶性的研究很感兴趣，因为该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。

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 last year 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 of 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 becomes a bad approximation to 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 issues, 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 may be necessary for understanding 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.