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

该奖项资助刘易斯与克拉克学院穆罕默德·安伯教授的研究活动。人们很早就知道原子核是由质子和中子组成的，而质子和中子又是由夸克组成的。后者是在一种叫做胶子的基本粒子的作用下粘在一起的。这种力非常强大，因此这种力被称为强核力，解释其工作原理的理论被称为量子色动力学（QCD）。不幸的是，由于QCD的强结合特性，人们对它的了解仍然很少。当原子核被加热时，就像在早期宇宙中或在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，即夸克-胶子等离子体。同样，由于核力的强大性质，人们对物质的这种状态知之甚少。最近，新的方法已经开发出来，最终将解开量子cd的一些秘密。一个有希望的方向涉及到称为高形式t - Hooft异常的某些数学结构，另一个方向借鉴了量子信息理论的思想。然而，对QCD中这些发展和它们之间的联系的完整理解还远远不够。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。这项研究符合国家利益，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重大的更广泛的影响，并对刘易斯和克拉克学院的课程发展产生直接影响。安伯教授将招募积极性很高的学生与他合作，并特别努力与女性和未被充分代表的少数民族接触。通过参与几个涉及数值模拟的项目，学生将为从事理论研究以及其他stem相关领域的职业做好准备。从技术上讲，在这个研究项目中，Anber教授将使用一种变形的类量子cd理论来阐明更高形式的t Hooft异常和纠缠熵。变形规范理论的一种新方法是在一个小圆上紧化它，应用扭曲的边界条件，和/或在高维表示中添加物质。这使原来的理论变成了一个弱耦合状态。变形的模型可能与成熟的四维理论绝热相连。然而，变形的一般方法和绝热连接理论仍然是一个悬而未决的问题。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中匹配高形式的异常。反常匹配条件还可用于搜索与原始四维理论绝热连接的一类变形模型。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t Hooft异常之间是否存在非平凡的联系。一种形式异常的存在表明真空是非平凡的，这可能导致基态纠缠熵的复杂结构。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.