Gauge Fields, Geometry, and Strings

规范字段、几何图形和字符串

• 批准号: 1620637
• 负责人: Christopher Beasley
• 金额: $ 18万
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620637&HistoricalAwards=false
• 关键词: Gauge; Fields; Geometry; Strings

This award funds the research activities of Professor Christopher Beasley at Northeastern University.According to modern particle physics, three of the four fundamental forces in Nature are expressed mathematically within the framework of certain types of theories known as gauge theories. These three forces are the electromagnetic force, the weak nuclear force (which is responsible for radioactive nuclear decays), and the strong nuclear force (which holds atomic nuclei together). The fourth fundamental force, gravity, stands as the notable exception. The discovery of gauge theories is undoubtably one of the great scientific achievements of the 20th century, crucial not only for our modern understanding of elementary particle physics but also for vast swaths of modern geometry and topology. Yet many foundational questions about the dynamics of gauge theory remain poorly understood. These questions have bearing on such topics as the structure of the proton, the character of dark matter and dark energy, or even the mechanism for high-temperature superconductivity. Professor Beasley will conduct research to develop new mathematical methods and tools, inspired by string theory, for analyzing a special class of gauge theories defined in two spatial dimensions. These gauge theories preserve supersymmetry, which relates particles of different spins to each other and is among the possible extensions of the Standard Model now being tested in experiments at the Large Hadron Collider (LHC). Research in this area thus advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical laws. The project will also have significant broader impacts. Substantial portions of the project involve joint work between Professor Beasley and his graduate students. The project thereby serves to train the next generation of mathematical physicists in the methods of quantum field theory and string theory, as well as to disseminate those methods more broadly throughout the mathematical community. Professor Beasley will also give a series of popular scientific talks for first-year undergraduates, will supervise junior and senior mathematics majors in a Research Capstone, and will videotape his lectures in a graduate course on quantum field theory for mathematicians.More technically, Professor Beasley will study perturbative and non-perturbative properties of supersymmetric Wilson loop operators associated to Legendrian knots in contact three-manifolds. He will investigate a relation between these operators and infinite-dimensional symmetry algebras known to occur in two-dimensional quantum field theory, as well as a new localization method for Feynman integrals. Professor Beasley will also construct a novel, time-dependent topological supersymmetry on three-manifolds which fiber over the circle. These ingredients will be applied to perform a variety of exact computations in gauge theory. The project invokes deep notions from contact geometry and topology, and so will establish further interdisciplinary connections between theoretical physics and mathematics.

该奖项资助了东北大学克里斯托弗·比斯利（Christopher Beasley）教授的研究活动。根据现代粒子物理学的考验，自然界中四个基本力量中的三个在数学上以某些类型的理论理论的框架表示。 这三种力是电磁力，弱核力量（负责放射性核衰减）和强核力（将原子核保持在一起）。 第四个基本力量，重力是值得注意的例外。 衡量理论的发现无疑是20世纪的伟大科学成就之一，这不仅对于我们对基本粒子物理学的现代理解，而且对现代几何和拓扑的广泛理解至关重要。 然而，许多有关仪表理论动力学的基本问题仍然很熟悉。 这些问题涉及诸如质子的结构，暗物质和暗能量的特征，甚至是高温超导性的机制。 Beasley教授将进行研究，以开发灵感来自字符串理论的新数学方法和工具，以分析在两个空间维度中定义的特殊仪表理论。这些规格理论保留了超对称性，该理论将不同自旋的颗粒彼此相关，并且是现在在大型强子对撞机（LHC）实验中测试的标准模型的可能扩展之一。 因此，该领域的研究通过以最基本的方向之一来促进科学的进步来提高国家利益：对新物理定律的发现和理解。 该项目还将产生更大的影响。 该项目的很大一部分涉及比斯利教授和他的研究生之间的共同工作。 因此，该项目在量子场理论和弦理论的方法中训练下一代数学物理学家，并在整个数学社区中更广泛地传播这些方法。 Beasley教授还将为一年级的本科生提供一系列流行的科学演讲，将在一项研究顶峰中监督初级和高级数学专业专业，并将在数学家的量子现场理论研究生课程中进行录像。三个manifolds。 他将研究这些操作员与已知发生在二维量子场理论中的无限二维对称代数之间的关系，以及Feynman积分的新定位方法。 Beasley教授还将在三个manifolds上构建一种新颖的，时间依赖的拓扑超对称性，该式纤维在整个圆圈上。 这些成分将应用于仪表理论中的各种精确计算。 该项目引用了接触几何和拓扑的深刻概念，因此将在理论物理学和数学之间建立进一步的跨学科联系。