Theoretical Particle Physics at City University

随着大型强子对撞机登上粒子物理竞技场，理论粒子物理学发现自己处于一个关键时刻。一方面，标准模型最后一个缺失的元素希格斯玻色子需要被找到，另一方面，LHC实验可能会发现超越标准模型的新粒子和过程。与此同时，在理论物理学界，有许多悬而未决的问题将受益于我们期望从LHC获得的信息。本项目将研究现代理论物理学中的两个关键问题。首先，我们将使用所谓的规范/弦对应来研究强耦合规范理论。关于强耦合规范理论还有许多东西要学。近年来，在利用规范弦对应来理解某些规范理论方面有了重大突破。特别是，被称为可积性的数学工具为某些超对称强相互作用规范理论提供了令人难以置信的精确分析处理。这些工具已经被证明可以扩展到相对较少的超对称性的某些设置。通过所谓的二聚体模型，低超对称规范理论也被证明与代数几何和代数数论的数学有着密切的联系。在这个项目中，我们将在这些结果的基础上，开发新的数学工具和方法，以理解更少的超对称规范理论及其规范/弦对偶的强耦合动力学。其次，我们将探索超越标准模型的物理学，它可以从弦理论中获得一致的低能理论。弦理论提供了一个框架，把规范和引力相互作用统一到一个统一的量子理论中。关键的挑战之一是确定弦理论紧致化的具体例子，这将导致现实的低能物理。我们的小组将系统地搜索大量的一致弦真空，寻找那些与标准模型和LHC发现的任何新物理学一致的模型。我们过去的经验表明，能够给出标准模型的弦几何是非常罕见的。这反过来又暗示了弦真空的独特性，而不是巨大的简并性，我们的目标是广泛地测试这个假设。

With the arrival of the LHC on the Particle Physics arena, theoretical particle physics finds itself at a critical juncture. On the one hand, the last missing element of the Standard Model, the Higgs boson, needs to be found, and on the other, the LHC experiments may find new particles and processes that go beyond the standard model. At the same time, in the theoretical physics community there are a number of outstanding problems that will benefit from the information that we expect to arrive from the LHC. This project will investigate two key problems in modern theoretical physics. Firstly, we will investigate strongly coupled gauge theories using the so-called gauge/string correspondence. Much remains to be learnt about strongly coupled gauge theories. In recent years, there have been significant breakthroughs in understanding certain gauge theories using the gauge/string correspondence. In particular, the mathematical tools known as integrability have provided an incredibly precise analytic handle on certain supersymmetric strongly interacting gauge theories. These tools have been shown to extend to certain settings with relatively little supersymmetry. Low-supersymmetry gauge theories have also been shown, through the so-called dimer models to have intimate links to the mathematics of algebraic geometry and algebraic number theory. In this project we will significantly build on these results to develop new mathematical tools and methods to understand the strong-coupling dynamics of less supersymmetric gauge theories and their gauge/string dualities.Secondly, we will explore beyond-the-Standard-Model physics that can be obtained as a consistent low-energy theory from string theory. String theory has provided a framework for unifying gauge and gravity interactions into a single consistent quantum theory. One of the key challenges has been to identify particular examples of string theory compactifications which will lead to realistic low-energy physics. Our group will systematically search through the very large number of consistent string vacua, for those models which are consistent with the Standard Model and any new physics found by the LHC. Our past experience suggests that stringy geometries which could give the Standard Model are very rare. This in turn hints at the uniqueness, rather than the huge degeneracy, of string vacua, and we aim to extensively test this hypothesis.