String Theory Scotland

自然界中有两种基本力：负责亚原子尺度上的粒子相互作用的力和负责宇宙大尺度结构的基本力。后者由爱因斯坦的广义相对论(GR)描述，而前者由标准模型等量子场论(QFT)描述。爱因斯坦的理论在概念上很简单，但却是经典的，当引力很强时，它就会崩溃，就像在非常小的尺度上一样，而QFT是有效的理论，它忽略了引力相互作用，在非常高的能量下是不可信的。在过去的三十年里，弦理论作为一个概念丰富的理论框架出现在GR和QFT之间。特别是，它是一个量子引力理论，我们小组的研究计划坚定地专注于弦理论的广泛的量子引力方面。宇宙的膨胀是无可争辩的。在弦理论中，宇宙通过弦背景的概念来描述。因此，如果弦理论要与宇宙学接触，就必须掌握依赖时间的背景，而这些背景并不直接适用于使用弦理论的标准微扰公式进行研究。我们小组率先研究依赖时间的弦背景，我们研究活动的一个重要部分就是围绕这一主题展开的。我们的目标是了解弦微扰理论在依赖时间的背景下的一般结构，以便能够回答诸如“弦理论能解决大爆炸类型的奇点吗？”-这是一个自然而然的问题，因为弦理论已知能解决其他类型的奇点。我们研究的另一个重要目标是推导弦理论的可观察到的宇宙学结果，以努力证伪它，或者至少限制可能的弦背景的景观。弦理论挑战了GR所依据的时空几何概念。在非常小的尺度上，时空的性质被认为与GR根本不同-它的连续结构被认为被离散的、不再区分个别时空事件的代数结构所取代。非对易几何(NCG)是现代数学中研究这种离散结构的一个分支。有强烈的迹象表明，NCG自然而然地出现在弦理论中，对这种预期的彻底调查是我们小组研究的另一个主要焦点。微扰弦理论是用二维共形场论(CFT)来描述的，我们在这一领域的主要目标之一是在一类重要的准有理共形场论上出现NCG。弦理论的低能量极限是超引力(Sugra)，它是GR的一个非平凡的扩展，其中宇宙是用带有额外几何数据的时空来描述的？这是弦物理的签名。随着能量的增加，这些背景被认为会得到修正，而确定哪种类型的修正是我们要解决的主要问题之一。正如在GR中一样，Sugra承认描述引力物体的解决方案，如黑洞、薄膜等。从霍金的工作中，我们知道黑洞遵循热力学定律，这就引出了一个自然的问题：黑洞的熵是由哪些微态来决定的？我们团队开创了对Sugra背景进行分类的系统方法，我们已经做好准备回答这一领域的一些更紧迫的问题，例如，在Sugra背景下，什么是可能的膜？这是Gauge/重力通信中的一个重要问题。总而言之，我们的研究涵盖了弦理论的广泛的引力方面，冲击了宇宙学、粒子物理学和弦理论本身的本质。

There are two types of fundamental forces in Nature: those responsible for particle interactions at subatomic scales and those responsible for the large scale structure of the universe. The latter is described by Einstein's General Theory of Relativity (GR) and the former by Quantum Field Theories (QFTs) such as the Standard Model. Einstein's theory is conceptually simple, but is classical and breaks down when the force of gravity is strong, as it is at very small scales, whereas QFTs are effective theories which ignore the gravitational interactions and which cannot be trusted at very high energies. During the last three decades, String Theory has emerged as a conceptually rich theoretical framework reconciling both GR and QFT. In particular, it is a theory of quantum gravity and our group's research programme is firmly focused on a wide range of quantum gravitational aspects of String Theory. The expansion of the universe is incontrovertible. In String Theory, the universe is described via the notion of a string background. Thus if String Theory is to make contact with cosmology, one has to come to grips with time-dependent backgrounds, which are not directly amenable to investigation using the standard perturbative formulation of string theory. Our group have pioneered the study of time-dependent string backgrounds and an important part of our research activities is centred on this topic. Our goal is to understand the general structure of string perturbation theory in time-dependent backgrounds in order to be able to answer questions such as 'Does string theory resolve Big-Bang-type singularities?'---a natural question in view of the fact that string theory is known to resolve other types of singularities. Another important goal of our research is to derive observable cosmological consequences of string theory in an effort to falsify it or at least to constraint the landscape of possible string backgrounds. String theory challenges the geometrical notions of spacetime on which GR is predicated. At very small ('stringy') scales the nature of spacetime is believed to be fundamentally different from GR---its continuous structures thought to be replaced by discrete, algebraic structures which no longer distinguish individual spacetime events. Noncommutative Geometry (NCG) is a branch of modern mathematics dealing with such discrete structures. There are strong hints that NCG appears naturally in String Theory and a thorough investigation of this expectation is another of the main focal points of our group's research. Perturbative string theory is described in terms of two-dimensional conformal field theory (CFT) and one of our main goals in this area is the emergence of NCG on the important class of quasi-rational conformal field theories. The low-energy limit of String Theory is supergravity (SUGRA), a nontrivial extension of GR, in which the universe is described by a spacetime with additional geometric data ? the signature of stringy physics. As the energy increases, these backgrounds are believed to receive corrections, and determining which types of corrections is one of the main questions we will address. As in GR, SUGRA admits solutions describing gravitating objects such as black holes, branes,... We known from Hawking's work that black holes obey the laws of thermodynamics and this prompts the natural question: 'Which microstates are responsible for the entropy of a black hole?' Our group have pioneered the systematic approach to the classification of SUGRA backgrounds and we are well poised to answer some of the more pressing questions in this area, such as 'what are the possible branes in a SUGRA background?', an important question in the gauge/gravity correspondence. In summary, our research encompasses a wide range of gravitational aspects of String Theory, impinging on cosmology, particle physics and on the very nature of String Theory itself.