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

该奖项资助刘易斯和克拉克学院的Mohamed Anber教授的研究活动。长期以来，人们一直知道原子核由质子和中子组成，而质子和中子又是由夸克组成的。后者在与称为胶子的基本粒子相关的力的影响下粘合在一起。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具有很强的约束性，人们对它的理解仍然很少。当原子核被加热时，就像在早期宇宙或地球人造实验中一样，夸克被解放并形成一种新的物质状态，称为夸克-胶子等离子体。同样，由于核力的强大性质，人们对这种物质状态的了解很少。最近，新的方法被开发出来，最终将揭开QCD的一些秘密。一个很有希望的方向涉及被称为更高形式t Hooft反常的某些数学结构，另一个方向借用了量子信息理论的想法。然而，在QCD中，对这些发展以及它们之间的联系的完全理解仍然远未完成。作为这个项目的一部分，Anber教授将开发新的技术，这些技术将揭示QCD的这些发展。这项研究具有国家利益，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开发产生直接影响。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。通过参与几个涉及数值模拟的项目，学生们将为在理论研究和其他STEM相关领域的职业生涯做好准备。更严格地说，在这个研究项目中，Anber教授将使用一类变形的QCD理论，以阐明更高形式的t Hooft反常和纠缠熵。一种使规范理论变形的新方法是将其压缩到一个小圆上，应用扭曲的边界条件，和/或在高维表示中添加物质。这将最初的理论带到了一个弱耦合的区域。变形的模型可能与成熟的四维理论有绝热联系。然而，变形的一般方法和绝热连接理论的类别仍然是悬而未决的问题。由于形变理论是弱耦合的，PI将使用可靠的半经典和微扰技术来研究更高形式的反常如何在红外中匹配。反常匹配条件也可用于寻找与原始四维理论绝热相关的形变模型。PI还将研究各种变形模型中的纠缠熵，这一计算在强耦合区域非常困难。最后，PI将检验纠缠熵和这类理论中的‘t Hooft反常之间是否有重要的联系。一种形式反常的存在表明真空不是微不足道的，这可能导致基态纠缠熵的复杂结构。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.