RUI: Compactified Gauge Theories: Phase Structure, Strings, and Continuity

该奖项为刘易斯克拉克学院的穆罕默德·安伯教授的研究活动提供资金。&我们宇宙的可见部分是由原子组成的，特别是质子和中子。而质子和中子则是由夸克组成的，夸克通过强核力结合在一起。然而，强力如何将夸克结合在一起仍然是物理学中最令人困惑的问题之一。回答这个问题符合我们的国家利益，因为它将促进我们对自然的一个基本方面，即物质的起源和结构的认识。该项目将开发新技术，揭示强核力的性质。 一般来说，这种力很少被理解，主要是因为解释它的理论，即量子色动力学（QCD），具有复杂的数学结构。 Anber教授试图通过增加新的变形来修改QCD，这将使通过分析手段研究强力成为可能。 该研究项目也将对本科生和更广泛的社区产生更广泛的影响。Anber教授将招募积极性很高的学生与他合作，特别努力接触妇女和代表性不足的少数民族。Anber教授还将设计关于场论和计算物理的两门课程，并将他的研究中的几个有意义的例子带到课堂上。此外，他将在研讨会和会议上介绍他的研究成果，并将在其他大学和文科学院发表演讲。将参与拟议研究的本科生将通过会议上的演讲和海报传播他们的贡献。从技术上讲，Anber教授提出通过在圆上紧致QCD和/或在各种表示中添加物质来变形QCD，这引入了红外截止，使理论进入弱耦合状态，并使其适合于半经典处理。变形理论不是真实的世界。然而，希望通过研究这类模型，人们将获得对现实世界QCD的新见解。令人惊讶的是，对这类理论的研究表明，各种物理观测量在强耦合和弱耦合状态下具有相同的定性行为，这表明弱耦合和强耦合理论之间的连续性。这种被束缚的连续性是诱人的。然而，我们对这种连续性还远远没有完全理解，必须收集充分的证据来支持甚至反对这种连续性，才能达成这种理解。拟议的研究计划将提高我们的结构的紧凑规范理论的理解，并告知我们的限制和/或背后的原因的约束连续性。这项研究的目的是（1）对圆上的所有限制规范理论进行分类，并了解在这类理论的真空中形成的分子瞬子的结构，（2）研究圆上的热规范理论的相图，（3）在我们解压缩圆时跟踪物理观测量的行为，（4）比较和对比描述弱耦合和强耦合区域中的扩展对象（约束弦）的拓扑场论。面对现有的晶格数据的研究结果可能会产生一个新的视角结构的约束规范理论。

This award funds the research activities of Professor Mohamed Anber at Lewis & Clark College. The visible part of our Universe is made of atoms, in particular, protons and neutrons. Protons and neutrons, in turn, are made of quarks, which are held together by what is known as the strong nuclear force. However, how the strong force holds the quarks together is still one of the most puzzling questions in physics. It is in our national interest to answer this question as it will advance our knowledge about one of the fundamental aspects of nature, namely the origin and structure of matter. This project will develop new techniques that will shed light on the nature of the strong nuclear force. In general, this force is poorly understood primarily because the theory that explains it, namely quantum chromodynamics (QCD), has a complex mathematical structure. Professor Anber seeks to modify QCD by adding new deformations that will make it possible to study the strong force by analytical means. This research project will also have significant broader impacts on undergraduate students and the broader community. Professor Anber will recruit highly motivated students to collaborate with him, making special efforts to reach out to women and underrepresented minorities. Professor Anber will also design two courses on field theory and computational physics, and several meaningful examples from his research will be brought to the classroom. In addition, he will present the results of his research in workshops and conferences and will give talks at other universities and liberal-arts colleges. The undergraduate students who will participate in the proposed research will disseminate their contributions through talks and posters in conferences. More technically, Professor Anber proposes to deform QCD by compactifying QCD on a circle and/or adding matter in various representations, which introduces an infrared cutoff that brings the theory into a weakly coupled regime and makes it amenable to semi-classical treatment. The deformed theory is not the real world. It is hoped, however, that by studying this class of models, one will gain new insights into real-world QCD. Surprisingly enough, studies of this class of theories have shown that various physical observables have the same qualitative behavior both in the strongly- and weakly-coupled regimes, suggesting continuity between weakly- and strongly-coupled theories. This conjectured continuity is tantalizing. However, we are still far from a complete understanding of this continuity, and ample evidence in support of or even against it has to be collected before such an understanding can be reached. The proposed research program will enhance our understanding of the structure of compactified gauge theories and inform us about the limitations of and/or reasons behind the conjectured continuity. The proposed study aims to (1) classify all confining gauge theories on a circle and understand the structure of the molecular instantons that form in the vacuum of this class of theories, (2) study the phase diagram of thermal gauge theories on a circle, (3) track the behavior of physical observables as we decompactify the circle, and (4) compare and contrast the topological field theories that describe the extended objects (confining strings) in the weakly- and strongly-coupled regimes. Confronting the results of the proposed study with the available lattice data may yield a new perspective on the structure of confining gauge theories.