String Theory, Gauge Theory and Duality

在当前的高能物理实验中研究的物质的基本成分看起来像是点状物体。到目前为止，这些粒子之间的相互作用被一个被称为量子场论的理论框架成功地描述了，规范理论是建立粒子物理标准模型(SM)的一个重要例子。在大尺度上，爱因斯坦的广义相对论很好地解释了我们宇宙的行为，广义相对论是一种用几何术语描述引力的经典场论。然而，随着大型强子对撞机(LHC)进入发现阶段，以及普朗克空间天文台正在收集高精度数据，我们目前的理论很快将面临一些新的严格考验。人们普遍预期，SM和广义相对论最终都只能以一种近似的方式描述现实。弦理论可以被看作是SM所基于的场论框架的推广：在弦理论中，基本成分是可以振动的一维或多维物体(即弦和膜)。弦理论暗示了关于SM的一些令人惊讶的新特征，例如额外空间维度的存在和物质与力之间的一种新类型的对称(超对称)。此外，虽然该理论在很大程度上与广义相对论一致，但它预测在引力的描述上也会有有趣的新奇之处。玛丽女王的研究旨在扩大我们在概念和计算层面上的弦和量子场理论知识。弦理论的一个令人惊讶的特点是它能够产生新的想法和技术，可以在不同的背景下使用。最近的一个与当前提议相关的例子是胶子之间某种类型的相互作用(MHV振幅)之间的弦激发关系，以及寻找其边界是特定多边形的区域的几何问题。QM的研究有助于理解这种关系，并正在积极研究新的、强大的方法来计算振幅，而不是使用传统的费曼图方法。特别注意规范理论的一种非常特殊的情况，即N=4的超杨-米尔斯。这些新技术正在被推广到处理物理幅度以外的其他有趣的量，并被应用于不同的量子场理论。N=4的超杨-米尔斯理论的一个令人惊讶的性质是，它在负曲线几何上传播的弦和膜具有完全等价的双重描述。自从马尔达塞纳发现这种二元性(ADS/CFT)以来，弦理论和量子场理论之间的“全息”关系已经得到了深入的研究。玛丽女王大学的研究旨在推导出这一理论的规范公式和弦理论公式之间的精确词典，并理解这种二元性的数学基础。QM正在从ADS/CFT的角度和更一般的弦/M理论的背景下分析弦和膜的动力学。这导致了关于黑洞的物理性质、明显不同的理论之间的对偶关系以及时空本身的几何性质的新的概念性结果。上述研究领域的进展可能与不同的科学领域非常相关。宇宙学是可以从我们目前的研究中受益的学科之一，QM正在研究弦理论在这一领域的各种应用。粒子物理学和大型强子对撞机数据的分析将受益于计算胶子振幅的新技术。与ADS/CFT二元性相关的理论思想也被QM用来分析有趣的凝聚态系统。最后，在从几何到群论的各个领域，数学和弦论之间存在着有益的思想交流。

The elementary constituents of matter studied in current high-energy physics experiments appear as point-like objects. The interactions among these particles are so far successfully described by a theoretical framework known as quantum field theory, gauge theories being an important example for the formulation of the particle physics Standard Model (SM). At large scales, the behaviour of our Universe is well explained by Einstein's General Relativity, a classical field theory describing gravity in geometrical terms. However, as the Large Hadron Collider (LHC) is entering its discovery phase and the Planck Space Observatory is harvesting high precision data, our current theories will soon face some new stringent tests. It is widely expected that both the SM and General Relativity turn out to describe reality only in an approximate fashion. String theory may be seen as a generalisation of the field theory framework on which the SM is based: in string theory the fundamental constituents are one- or multi-dimensional objects (i.e. strings and branes) that can vibrate. String theory implies some surprising new features with respect to the SM, such as the existence of extra space-dimensions and a new type of symmetry between matter and forces (supersymmetry). Moreover, while at large distances the theory agrees with General Relativity, it predicts interesting novelties also in the description of the gravitational force. Research at Queen Mary aims to expand our knowledge of string and quantum field theories both at the conceptual and the computational level. A surprising feature of string theory is its ability to generate new ideas and techniques that can be employed in different contexts. A recent example of this, which is relevant for the current proposal, is the string inspired relation between a certain type of interaction among gluons (MHV amplitudes) and the geometrical problem of finding the area whose boundary is a particular polygon. Research at QM contributed to the understanding of this relation and is actively studying new and powerful ways to calculate amplitudes without using the traditional approach of Feynman diagrams. Particular attention is devoted to a very special case of the gauge theory, known as N=4 super Yang-Mills. These new techniques are being generalised to handle other interesting quantities beyond the physical amplitudes and are being applied to different quantum field theories. A surprising property of N=4 super Yang-Mills theory is that it has a completely equivalent, dual description in terms of strings and branes propagating on negatively curved geometries. Since Maldacena's discovery of this duality (AdS/CFT), the 'holographic' relation between string and quantum field theories has been thoroughly studied. Research at Queen Mary aims to derive the precise dictionary between the gauge and the string theory formulations of this theory and to understand the mathematical basis of this duality. The dynamics of string and branes is being analysed at QM both from the AdS/CFT perspective and in the more general string/M-theory context. This is leading to new conceptual results about the physical properties of black holes, the duality relations between apparently different theories and the geometrical properties of space-time itself. Advances in the research areas mentioned above are likely to be very relevant in different areas of science. Cosmology is one of the subjects that can benefit from our current research and various applications of string theory to this field are being studied at QM. Particle physics and the analysis of LHC data will benefit from new techniques developed to calculate gluon amplitudes. Theoretical ideas related to the AdS/CFT duality are also being used at QM to analyse interesting condensed matter systems. Finally there is a beneficial flow of ideas between mathematics and string theory in various areas ranging from geometry to group theory.