RUI: Higher-Form 't Hooft Anomalies, Information Theory, and Continuity in Gauge Theories

RUI：更高形式的特霍夫特异常、信息论和规范理论的连续性

• 批准号: 2013827
• 负责人: Mohamed Anber
• 金额: $ 13.5万
• 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: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2013827&HistoricalAwards=false
• 关键词: RUI; Higher; Form; Hooft; Anomalies

This award funds the research activities of Professor Mohamed Anber at Lewis and Clark College.It has been known for a long time that the atomic nucleus consists of protons and neutrons which in turn are made of quarks. The latter are glued together under the influence of a force associated with elementary particles called gluons. This force is tremendously strong, and hence this force is known as the strong nuclear force and the theory that explains how it works is known as quantum chromodynamics (QCD). Unfortunately, QCD remains poorly understood, thanks to its strong-binding nature. When nuclei are heated, as in the early Universe or in terrestrial man-made experiments, the quarks are liberated and form a new state of matter known as a quark-gluon plasma. Again, this state of matter is poorly understood due to the strong nature of the nuclear force. Recently, new methods have been developed which will ultimately unlock some of the secrets of QCD. One promising direction involves certain mathematical structures called higher-form 't Hooft anomalies, and another direction borrows ideas from quantum information theory. A complete understanding of these developments and the linkages between them in QCD, however, is still far from complete. As part of this project, Professor Anber will develop novel techniques that will shed light on these developments in QCD. This research is of national interest as it advances our understanding of the fundamental laws of nature. The project will also have significant broader impacts for students and the broader community and have a direct impact on curriculum development at Lewis and Clark College. Professor Anber will recruit highly motivated students to collaborate with him, making special efforts to reach out to women and underrepresented minorities. By participating in several projects involving numerical simulations, students will be prepared for careers in theoretical research as well as other STEM-related fields.More technically, in this research project, Professor Anber will use a deformed class of QCD-like theories in order to shed light on higher-form 't Hooft anomalies and entanglement entropy. A novel approach to deforming a gauge theory is to compactify it on a small circle, apply twisted boundary conditions, and/or add matter in higher-dimensional representations. This brings the original theory to a weakly coupled regime. The deformed models may be adiabatically connected to full-fledged four-dimensional theories. However, the general means of deformations and the class of adiabatically-connected theories remain open questions. Since the deformed theory is weakly coupled, the PI will use reliable semi-classical and perturbation techniques to investigate how the higher-form anomalies are matched in the infrared. The anomaly-matching conditions can also be used to search for the class of deformed models that are adiabatically connected to the original four-dimensional theories. The PI will also investigate entanglement entropy in various deformed models, a calculation that is prohibitively difficult in the strong-coupling regime. Finally, the PI will examine whether there are nontrivial connections between entanglement entropy and 't Hooft anomalies in this class of theories. The existence of one-form anomalies indicates that the vacuum is nontrivial, which can lead to a complex structure in the entanglement entropy of the ground state.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项资助了刘易斯和克拉克学院的穆罕默德·安伯教授的研究活动。很久以前就知道，原子核由质子和中子组成，而质子和中子又由夸克组成。 后者在一种与基本粒子胶子有关的力的影响下粘在一起。 这种力非常强大，因此这种力被称为强核力，解释它如何工作的理论被称为量子色动力学（QCD）。 不幸的是，由于其强约束性，QCD仍然知之甚少。 当原子核被加热时，就像在早期宇宙或地球上的人造实验中一样，夸克被释放出来，形成一种新的物质状态，称为夸克-胶子等离子体。 同样，由于核力的强性质，这种物质状态的理解很少。 最近，新的方法已经开发出来，最终将揭开QCD的一些秘密。 一个有希望的方向涉及某些被称为高级形式特胡夫特反常的数学结构，另一个方向借鉴了量子信息理论的思想。 然而，对这些发展以及它们之间在QCD中的联系的完整理解还远远没有完成。作为该项目的一部分，Anber教授将开发新的技术，以阐明QCD的这些发展。 这项研究是国家利益，因为它促进了我们对自然基本规律的理解。 该项目还将对学生和更广泛的社区产生更广泛的影响，并对刘易斯和克拉克学院的课程开发产生直接影响。 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。 通过参与几个涉及数值模拟的项目，学生将为理论研究以及其他STEM相关领域的职业生涯做好准备。更技术性的是，在这个研究项目中，Anber教授将使用一种变形的类QCD理论，以揭示更高形式的't Hooft异常和纠缠熵。 变形规范理论的一种新方法是将其紧致化在一个小的圆上，应用扭曲的边界条件，和/或在高维表示中添加物质。 这使原来的理论弱耦合的制度。 变形的模型可以在理论上与成熟的四维理论联系起来。然而，变形的一般方法和绝热连接理论的类仍然是悬而未决的问题。由于变形理论是弱耦合的，PI将使用可靠的半经典和微扰技术来研究如何在红外线中匹配更高形式的异常。异常匹配条件也可以用来搜索与原始四维理论有联系的变形模型类。 PI还将研究各种变形模型中的纠缠熵，这在强耦合状态下是非常困难的计算。 最后，PI将研究在这类理论中，纠缠熵和特胡夫特反常之间是否存在非平凡的联系。单一形式异常的存在表明真空是不平凡的，这可能导致基态纠缠熵的复杂结构。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。