Defects and Extended Objects in Quantum Field Theory and Quantum Gravity

这个奖项资助了纽约大学王一凡教授的研究活动。物质很少以纯物质的形式出现在自然界中。更常见的是，它是多种成分的复杂混合物。在物质几乎是均匀的情况下，剩余的不规则或不连续性被称为缺陷。物理上有趣的缺陷的例子范围从日常生活中遇到的那些，如悬浮在牛奶中的脂肪滴和金属中的杂质原子，到极端的情况，如在称为夸克胶子等离子体的奇异物质状态中的重粒子，巨大的热量和压力将原子核压碎，形成基本粒子汤。已经发现，缺陷对材料的物理行为具有深远的影响，引起新的相变和临界现象，并提供用于检测物质相的灵敏探针。理论物理学的一个重要挑战是开发分析缺陷及其性质的工具。量子场论可以说是具有大量组成元素的系统的最成功的物理理论，它提供了描述缺陷的自然框架。然而，量子场论的大部分成功都是建立在对称性和定域性的基本原理上的，而引入缺陷则需要对这些原理进行改进。这反过来又揭示了大量需要理解的复杂数学结构。王教授旨在通过追求以下问题来推进量子场论中缺陷的理解：我们如何预测缺陷的影响？缺陷的性质是否有普遍的模式？缺陷的行为背后是否有原则？解决这些问题将促进科学的进步，并通过潜在的发现和理解新的物理定律来促进国家利益。王教授的工作也将产生更广泛的影响，包括开发新课程，培训本科生和研究生，以及通过这些项目的合作指导博士后研究人员。更技术上，王教授的目标是从多个互补的角度深入研究量子场论的缺陷。这包括推导出通用的约束条件来描绘可接受的缺陷的景观，开发分析工具来访问缺陷的可观察性和澄清其功能，并探索广义对称性和异常缺陷。通过著名的全息对偶性，普通量子多体系统中的缺陷也与量子引力中的扩展对象密切相关，称为膜（如弦论中的D膜）。这些膜对于量子引力在非微扰水平上的一致性是必不可少的，但是这些膜的光谱和动力学仍然没有得到充分的探索。在他的场论探索缺陷的同时，王教授还计划推导量子引力中非微扰膜的结果。为了实现上述目标，一个技术的组合将采用和进一步发展沿着的方式，包括共形引导，拓扑场论，超对称性，可积性，和大N极限。拟议工作的一个直接影响将是量子场论中扩展算子代数的综合视角，其中包括缺陷，以及对高能和凝聚态系统中重整化群流的更好理解。另一个有希望的成果是对弦理论中的（非超对称）D膜和量子引力中更一般的扩展对象进行系统分析。该奖项反映了NSF的法定使命，并被认为值得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来支持。

This award funds the research activities of Professor Yifan Wang at New York University.Matter rarely appears in nature as a pure substance. More commonly it exists as a complex mixture of multiple components. In cases when the matter is almost homogenous, the remaining irregularities or discontinuities are known as defects. Examples of physically interesting defects range from those encountered in daily life such as fat droplets suspended in milk and impurity atoms in metals, to extreme scenarios such as heavy particles in an exotic state of matter known as the quark-gluon plasma where immense heat and pressure crush the nuclei to make a soup of elementary particles. It has been found that defects have profound consequences for the physical behavior of the materials, give rise to novel phase transitions and critical phenomena, and provide sensitive probes for detecting phases of matter. An important challenge in theoretical physics is to develop tools to analyze defects and their properties. Quantum field theory, which is arguably the most successful physical theory for systems with a large number of constituent elements, provides the natural framework to describe defects. However much of the success of quantum field theory dwells on the fundamental principles of symmetry and locality, and to incorporate defects requires a refinement of these principles. This in turn uncovers an abundance of intricate mathematical structures to be understood. Professor Wang aims to advance the understanding of defects in quantum field theory by pursuing the following questions: How do we predict the effects from the defects? Are there universal patterns in the properties of defects? Are there principles behind how defects behave? Addressing these questions would promote the progress of science and advance the national interest by potentially discovering and understanding new physical laws. Professor Wang's work will also produce broader impacts in the form of the development of new courses, training undergraduate and graduate physics students, as well as mentoring postdoctoral researchers through collaborations on these projects.More technically, Professor Wang aims to pursue a thorough investigation of defects in quantum field theory from multiple complementary angles. This includes deriving universal constraints to delineate the landscape of admissible defects, developing analytic tools to access defect observables and clarify their features, and exploring generalized symmetries and anomalies from defects. By the celebrated holographic duality, defects in ordinary quantum many-body systems are also closely related to extended objects in quantum gravity, known as branes (such as D-branes in string theory). These branes are essential for the consistency of quantum gravity at the non-perturbative level, but the spectrum and dynamics of such branes remain under-explored. In parallel to his field-theoretic exploration of defects, Professor Wang also plans to deduce consequences for the non-perturbative branes in quantum gravity. To achieve the aforementioned goals, a combination of techniques will be employed and further developed along the way, including conformal bootstrap, topological field theory, supersymmetry, integrability, and large-N limits. One immediate impact of the proposed work will be an integrated perspective of the extended operator algebra in quantum field theory that incorporates defects, and an improved understanding of renormalization-group flows in both high-energy and condensed-matter systems. Another promising outcome would be a systematic analysis of (non-supersymmetric) D-branes in string theory and more general extended objects in quantum gravity.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.