Heterotic string theory

我建议写一篇弦理论的论文。更具体地说，我将研究杂交链真空体的一致性。粒子物理的标准模型和广义相对论在各自的领域都是非常成功的理论，但如果我们要有一个包含这两个理论的一致的量子理论，那么我们似乎不可避免地会出现弦理论。虽然弦理论很可能是不完整的，但在撰写本文时，似乎还没有任何可行的替代方案。在弦理论中，有一类真空，即杂化真空，似乎最接近于观察到的粒子物理的四维世界。尽管早在1985-1986年的“弦革命”中就已经知道真空的存在或这些真空的存在，但人们对这种真空的详细了解却很少。我们首先利用半经典论证提出了这些真空，直到最近，无论是在寻找可能现实的杂化真空的显式例子方面，还是在这些真空是否真的存在于量子水平上，都取得了相对较小的进展。这里的一个重要问题是，如果微扰异质真空要作为理论的真正真空而存在，理论中的某些汤川耦合必须消失。我建议在这方面写一篇论文。主要问题是杂种真空体是否真的存在。如果他们这样做了，那么一个重要的问题是找到这样一个描述真实世界的真空。上面提到的汤川耦合实际上是(半经典)真空参数之间的耦合。因此，重要的第一步是正确识别这些参数。这里仍有工作要做，但在最近的文件中已经迈出了重要的一步。我将尝试推广这些论文中的几何方法。我的第一个研究主题将是检查与这些参数相关的经典汤川耦合，并(希望)验证耦合在真空的真实参数之间的事实，以确保相关耦合为零。第二个问题将是检查量子校正耦合是否也消失了。这是比较困难的，因为对耦合的量子校正是由瞬子贡献产生的，并且有已知的例子，其中对给定耦合的单个瞬子贡献是非零的，但所有瞬子贡献的总和导致结果为零。目前，取消现象还很神秘，我的目标是了解真空是什么时候以及为什么是真空。这项工作的影响将首先在物理学家和数学家中产生。然而，由于寻求的是在弦理论和粒子物理的观察世界之间建立联系，这个目标的重要性怎么强调都不为过。这个项目属于EPSRC数学物理研究领域

I propose writing a dissertation in string theory. More specifically, I will examine the consistency of heterotic string vacua. Both the standard model of particle physics and general relativitity are highly successful theories in their respective domains but if we are to have a consistent quantum theory that encompasses both of them it seems inevitable that we are led to string theory. While string theory may well be incomplete, at the time of writing, there does not seem to be any viable alternatives.Within string theory, there are a class of vacua, the heterotic vacua, that seem closest to the observed four dimensional world of particle physics. Despite the fact that the existence or these vacua has been knwon since early in the "string revolution" of 1985-1986, very little is known in detail about such vacua. These vacua we first proposed using semi-classical arguments and relatively little progress has been made until recently either with respect to finding explicit examples of heterotic vacua that might be realistic or even whether these vacua really exist at the quantum level. A significant issue here is that certain Yukawa couplings in the theory have to vanish if the perturbative heteroticvacuum is to exist as a true vacuum of the theory. I propose writing a thesis in this area. The main question is whether heterotic vacua really exist. If they do, then an importantquestion is to find such a vacuum that describes the real world. The Yukawa couplings referred to above are, in reality, couplings between the parameters of the (semi-classical) vacua. An important first step is therefore to correctly identify these parameters. Workremains to be done here but a significant step has been taken in recent papers. I will try to extend the geometrical methods found in these papers.My first research topic will be to check the classical Yukawa couplings associated with these parameters and (hopefully) verify the fact that the couplings are between true parameters of the vacuum ensures that associated couplings vanish. A second problem will be to check that the quantum corrected couplings also vanish. This is more difficult since the quantum corrections to the couplings result from instanton contributions and there are known examples where the individual instanton contributions to a given coupling are non-zero but the sum over all instanton contributions leads to a vanishing result.[4]. At present the cancellations are mysterious and my aim would be to understand whenand why the vacua are the vacua.The impact of this work will in the first instance, be among physicists and mathematicians. However, since what is sought is to make contact between string theory and the observed world of particle physics, it is hard to overstate the importance of this aim.This project falls within the EPSRC Mathematical Physics research area