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

RUI：紧缩规范理论：相结构、弦和连续性

基本信息

批准号：
1720135
负责人：
Mohamed Anber
金额：
$ 7.93万
依托单位：
Lewis and Clark College
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720135&HistoricalAwards=false
关键词：
RUI Compactified Gauge Theories Phase

项目摘要

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.

该奖项资助刘易斯和克拉克学院的穆罕默德·安伯教授的研究活动。我们宇宙的可见部分是由原子组成的，特别是质子和中子。反过来，质子和中子是由夸克组成的，夸克被称为强大的核力将它们聚集在一起。然而，强大的引力如何将夸克聚集在一起，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的认识，即物质的起源和结构。该项目将开发新的技术，以揭示强大核力量的性质。一般来说，人们对这种力知之甚少，主要是因为解释它的理论，即量子色动力学(QCD)，有一个复杂的数学结构。Anber教授试图通过添加新的形变来修改QCD，这将使用解析方法研究这种强大的力成为可能。这项研究项目也将对本科生和更广泛的社区产生重大而广泛的影响。安贝尔教授将招募积极进取的学生与他合作，特别努力接触女性和代表性不足的少数族裔。Anber教授还将设计两门关于场论和计算物理的课程，他的研究中的几个有意义的例子将被带到课堂上。此外，他将在研讨会和会议上展示他的研究成果，并将在其他大学和文理学院发表演讲。将参与这项研究的本科生将通过演讲和在会议上张贴海报来传播他们的贡献。在更严格的技术层面上，Anber教授建议通过在圆上压缩QCD和/或在不同的表示中添加物质来使QCD变形，这引入了红外截止，使该理论进入弱耦合区域，并使其适合于半经典处理。畸形的理论并不是真实世界。然而，人们希望通过研究这类模型，人们将对现实世界的QCD有新的见解。令人惊讶的是，对这类理论的研究表明，在强耦合和弱耦合区域，各种物理可见具有相同的定性行为，这表明弱耦合和强耦合理论之间存在连续性。这种猜测的连续性令人着迷。然而，我们仍远未完全理解这种连续性，必须收集足够的证据支持甚至反对这种连续性，才能达成这样的理解。拟议的研究计划将加强我们对紧致规范理论结构的理解，并让我们了解假设连续性的局限性和/或背后的原因。这项研究的目的是(1)对圆上的所有约束规范理论进行分类，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)在我们分解圆的过程中跟踪物理可见项的行为；(4)比较和对比描述弱耦合和强耦合状态下扩展物体(禁闭弦)的拓扑场理论。用现有的晶格数据来正视所提出的研究结果，可能会对约束规范理论的结构产生一个新的视角。