Phase structure of strongly coupled field theories and gravity

粒子理论的基石之一是用所谓的规范场论来描述基本粒子和它们之间的力。用“量子色动力学”（QCD）描述将夸克束缚在质子和中子中的强力是该计划的重大成就之一。这一理论已经在粒子加速器的高能实验中得到了严格的检验。然而，在较低的能量下，夸克之间的相互作用变得更强，QCD变得越来越难以分析。我们对夸克如何被限制在质子和中子中的理解主要是基于困难的数值模拟。更好地理解场论中的这种强耦合机制是基础理论研究的一个关键目标。弦理论为强耦合场论提供了一种质的新方法。基于之前对弦论中黑洞的基本描述的研究，马尔达西纳指出，对于某些场论来说，在高维弯曲时空中传播的弦有一个等价的描述。场论所处的空间与弦运动的空间边界相关联。这个猜想把我们在粒子物理学中研究的场论和弦论中对引力的描述联系了起来。这对这两个地区来说都非常令人兴奋。对于弦理论，它提供了一个更基本的描述，首次涵盖了物理过程的全部范围。对于场论来说，它提供了一个有效的计算工具，可以用来研究强耦合情况下的场论。场论中的许多难题在弦论的描述中变得出奇地简单，反之亦然。最近，在研究QCD有限温度行为的实验的推动下，人们对使用这些技术研究有限温度下的场论重新产生了兴趣（尽管通过Maldacena对应描述引力的场论并不具有真实的QCD的所有特征）。场论的有限温度阶段与在黑洞时空中运动的弦有关。我们已经广泛地研究了这种黑洞时空的性质，以及从场论的角度对它们的描述。我们在这个项目中的目标是应用我们现有的专业知识在重力方面的对应，以促进这些领域的理论问题的更深入的理解，并探索扩展到包括自然出现在最近构建的重力解决方案的影响。高维黑洞是一个非常丰富的物理系统，我们希望这在场论物理学中有有趣的反映。

One of the cornerstones of particle theory is the description of elementary particles and the forces between them in terms of what are called gauge field theories. The description of the strong force, which binds quarks together in protons and neutrons and is responsible for the stability of atomic nuclei, in terms of 'quantum chromodynamics' (QCD) is one of the great successes of this programme. This theory has been rigorously tested by high-energy experiments at particle accelerators. However, at lower energies the interaction between the quarks grows stronger, and QCD becomes increasingly difficult to analyse. Our understanding of how quarks are confined within the protons and neutrons is primarily based on difficult numerical simulations. A better understanding of this strong coupling regime in field theory is a key goal for basic theoretical research. A qualitatively new approach to strongly-coupled field theory has emerged from string theory. Building on previous research into the fundamental description of black holes in string theory, Maldacena conjectured that there was an equivalent description for certain field theories in terms of strings propagating in a higher-dimensional, curved spacetime. The space that the field theory lives in is associated with the boundary of the space that the strings move in. This conjecture makes a fascinating link between the kind of field theories we study in particle physics and the description of gravity in string theory. It is very exciting for both areas. For string theory, it provides a more fundamental description, which covers the full range of physical processes for the first time. For field theory, it provides an effective calculational tool which can be used to study field theories at strong coupling. Many problems which are difficult in the field theory become surprisingly simple in the string theory description, and vice-versa. Recently, there has been a renewed interest in using these techniques to study field theory at finite temperature, motivated by experiments studying the finite temperature behaviour of QCD (although the field theories which have a gravitational description through Maldacena's correspondence do not have all the features of real QCD). The finite-temperature phase of the field theory is related to strings moving in a black hole spacetime. We have worked extensively on the properties of such black hole spacetimes, and their description from the field theory point of view. Our aim in this project is to apply our existing expertise on the gravity side of the correspondence to contribute to a deeper understanding of these field theory issues, and to explore the extension to include effects which appear naturally in recently constructed gravity solutions. The higher-dimensional black holes are a very rich physical system, and we expect this to have interesting reflections in the physics of the field theories.