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Gauge Theory Amplitudes and String Theory in Twistor Space

扭量空间中的规范理论振幅和弦理论

基本信息

批准号：
EP/C544250/1
负责人：
Gabriele Travaglini
金额：
$ 25.31万
依托单位：
Queen Mary University of London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FC544250%2F1
关键词：
Gauge Theory Amplitudes String Twistor

项目摘要

One of the ultimate goals of modern theoretical physics is to discover the Theory of Everything, that is a unified description for the four apparently different forces we observe in nature: electromagnetic, weak, strong, and finally gravitational. In the 1970s, a theoretical framework was proposed which accomplishes the task of incorporating electromagnetism and the weak and strong force into a unified theory, the so-called Standard Model of fundamental interactions. This theory has passed many remarkable experimental tests, and has been studied in great detail thanks to powerful colliders, where particles are scattered at very high energy to study their interactions.Of the four fundamental forces of nature, gravity is the one we have the most experience of. It is however gravity which has escaped all attempts to be unified with the others for the longest time. Furthermore, and perhaps surprisingly, of all coupling constants - the number which, roughly speaking, quantifies the strength of the force - Newton's constant (related to the strength of gravity) is by far the smallest and also the one which is known with the smallest experimental precision. At present, there is only one theory which incorporates gravity with the forces of the Standard Model: this is String Theory. A musical analogue is appropriate here: When we hit a piano string, we not only produce the fundamental sound but also an infinite series of (less perceivable) overtones, or harmonics. In string theory, each harmonic corresponds to a different particle. Different harmonics have of course increasing frequency, and Quantum Mechanics taught us that frequency is proportional to energy. Energy is also related to mass, through Einstein's famous formula E=mc^2. Therefore all the particles in this infinite tower have an increasing mass.Actually string theory was discovered in a slightly different unification attempt. In the 1960s, a vast proliferation of particles had been discovered at particle colliders. Physicists tried to find an explanation for this mysterious fact, and thought that a theory of strings, with its infinite tower of particles, could be the solution to the puzzle. Representing a particle as the excitation of a string - an object with an intrinsic length - is a very different picture compared to the traditional concept of a particle as a pointlike object that we have been accustomed to since the time of Democritus. So it seems that we have two very different descriptions for the same object. What physicists realised in the last 30 years or so, is that many aspects of the interactions of particles can also be described by either resorting to the concept of point particle or to the alternative string description. The existence of two alternative descriptions is referred to as a duality between them.One could then ask why we need many descriptions of the same phenomena. Are we not satisfied with one, possibly the conventional one in terms of point particles, which seems to work pretty well? There are many possible answers to this objection. Firstly, having several different description of the same phenomenon leads inevitably to a deeper understanding of the phenomenon itself. Secondly, these different descriptions can be complementary, in the sense that one might work where the other fails. Another answer, directly relevant to this research project, is that the conventional approach of point particles (or Field Theory, in mathematical language) does not always account for the marvellous and unexpected simplicity of certain scattering amplitudes - quantities that physicists compute and can be measured experimentally at particle colliders. Unexplained beauty in mathematical formulae describing physical observables is often the hint of some deeper mathematical structure to be uncovered; string theory often plays the role of that deeper structure. By identifying new, simpler descriptions of known phenomena, we also gain a great deal in terms of computational power. This is crucial if we wish to discover new physics, which requires us to disentangle genuinely new phenomena from the processes due to Standard Model physics with great experimental precision. Edward Witten has recently discovered an example of duality which promises to be directly relevant for future experiments. It has already made it possible to dramatically increase our ability to compute phenomenologically interesting quantities. The study of this fascinating new duality, both on the field theory and on the string theory side, is the subject of my research proposal.

现代理论物理学的最终目标之一是发现万有理论，这是对我们在自然界中观察到的四种明显不同的力的统一描述：电磁力，弱力，强力，最后是引力。在20世纪70年代，一个理论框架被提出，它完成了将电磁学和弱力和强力纳入统一理论的任务，即所谓的基本相互作用标准模型。这一理论已经通过了许多了不起的实验测试，并且由于强大的对撞机而得到了非常详细的研究，在那里粒子以非常高的能量散射以研究它们的相互作用。在自然界的四种基本力中，引力是我们最有经验的一种。然而，在很长一段时间里，引力一直逃避着与其他事物统一的所有尝试。此外，也许令人惊讶的是，在所有耦合常数中--粗略地说，这个数量化了力的强度--牛顿常数（与引力的强度有关）是迄今为止最小的，也是已知的实验精度最小的。目前，只有一种理论将引力与标准模型的力结合起来：这就是弦理论。这里可以用一个音乐类比：当我们敲击钢琴弦时，我们不仅产生了基本音，还产生了无限系列的（不易察觉的）泛音或和声。在弦理论中，每个谐波对应一个不同的粒子。不同的谐波当然会增加频率，量子力学告诉我们频率与能量成正比。通过爱因斯坦著名的公式E=mc^2，能量也与质量相关。因此，这个无限塔中的所有粒子的质量都在增加。实际上，弦理论是在一个稍微不同的统一尝试中发现的。20世纪60年代，在粒子对撞机上发现了大量的粒子。物理学家们试图为这个神秘的事实找到一个解释，并认为一个拥有无限粒子塔的弦理论可能是这个难题的答案。把粒子表示为弦的激发--一个具有固有长度的物体--与我们自德谟克利特时代以来就习惯的把粒子表示为点状物体的传统概念相比，是一个非常不同的图景。所以我们似乎对同一个物体有两种截然不同的描述。物理学家在过去30年左右的时间里意识到，粒子相互作用的许多方面也可以通过诉诸点粒子的概念或替代的弦描述来描述。存在两种可供选择的描述被称为它们之间的二元性，于是人们可能会问，为什么我们需要对同一现象的许多描述。我们是否对一个，可能是点粒子方面的传统方法，不满意，它似乎工作得很好？对于这个反对意见，有许多可能的答案。首先，对同一现象进行几种不同的描述不可避免地会导致对现象本身的更深入的理解。其次，这些不同的描述可以是互补的，在这个意义上，一个可能在另一个失败的地方工作。另一个与本研究项目直接相关的答案是，传统的点粒子方法（或场论，用数学语言来说）并不总是能解释某些散射振幅的奇妙和意想不到的简单性-物理学家计算的量，可以在粒子对撞机上实验测量。描述物理观测量的数学公式中无法解释的美，往往暗示着某种更深层次的数学结构有待揭示;弦理论常常扮演着这种更深层次结构的角色。通过识别已知现象的新的、更简单的描述，我们在计算能力方面也获得了很大的收获。如果我们希望发现新的物理学，这是至关重要的，这要求我们以很高的实验精度从标准模型物理学的过程中解开真正的新现象。爱德华维滕最近发现了一个对偶性的例子，它有望与未来的实验直接相关。它已经使我们有可能极大地提高计算现象学上有趣的量的能力。我的研究计划就是要从场论和弦论两方面来研究这个迷人的新对偶性。