Quantum Field Theory for Topological Phases of Matter

该奖项资助石溪大学邵树恒教授的研究活动。对称性已经一次又一次地被证明是理论物理学的基本指导原则。应用范围从爱因斯坦狭义相对论中的时空对称性，到氢原子的量子力学描述中的旋转对称性，再到物质不同相的分类。对称性是分析具有强相互作用的量子系统的少数普遍适用的工具之一，它经常导致深远的动力学后果。近年来，对称性的概念在几个不同的方向上得到了推广，在高能物理、凝聚态物理、数学和量子信息理论中得到了跨学科的应用。邵教授的目标是建立一个现代的理论框架来讨论这些新的对称性，并揭示在各种物理系统中隐藏的对称性。沿着这条路线的研究通过加强美国的基础研究和解决科学中最基本和最基本的问题之一，即对称性的作用，促进了国家利益。预计该项目还将产生更广泛的重大影响。邵教授将通过合作研究项目指导博士后研究人员。他还计划以自己的研究成果为基础，进行公开演讲，并组织暑期学校。从技术上讲，邵教授将重点关注三种主要的广义全局对称：子系统对称、高形式对称和不可逆转对称之间的相互作用。子系统和更高形式的对称是不均匀作用于整个物理系统的新型对称，而不可逆转的对称与不能撤消的对称变换有关。邵教授将在量子场论和晶格模型的背景下研究这些对称性。在子系统对称性的背景下，他将这些对称性应用于物质的一个新的量子相，即所谓的“分数子”相，并扩展量子场论的框架来描述分数子的连续统极限。他还将研究与这些广义对称性相关的新异常，并推导重整化群流的非平凡约束。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 Professors Shu-Heng Shao at Stony Brook University.Symmetry has proven, time and again, to be the fundamental guiding principle in theoretical physics. Applications range from the spacetime symmetry in Einstein's theory of special relativity to the rotational symmetry in the quantum-mechanical description of the hydrogen atom and to the classification of the different phases of matter. Symmetry is one of the few universally applicable tools in analyzing quantum systems with strong interactions, and it often leads to far-reaching dynamical consequences. In recent years, the notion of symmetry has been generalized in several different directions, with interdisciplinary applications in high-energy physics, condensed-matter physics, mathematics, and quantum information theory. Professor Shao aims to develop a modern theoretical framework to discuss these new symmetries and uncover hidden symmetries in a diverse set of physical systems. Research along this line advances the national interest by reinforcing fundamental research in the United States and addressing one of the most fundamental and basic issues in the sciences, namely the role of symmetries. This project is also expected to have signiicant broader impacts. Professor Shao will mentor postdoctoral researchers through collaborations on proposed research projects. He also plans to give public lectures and organize summer schools based on his research.More technically, Professor Shao will focus on the interplay between three major kinds of generalized global symmetries: subsystem symmetries, higher-form symmetries, and non-invertible symmetries. Subsystem and higher-form symmetries are novel symmetries that do not act uniformly on the whole physical system, while non-invertible symmetries are associated with symmetry transformations that cannot be undone. Professor Shao will investigate these symmetries within the context of quantum field theory and lattice models. Within the context of subsystem symmetries, he will apply these symmetries to a new quantum phase of matter, the so-called "fracton" phase, and extend the framework of quantum field theory to describe the continuum limit of fractons. He will also study new anomalies associated with these generalized symmetries and derive nontrivial constraints on renormalization-group flows.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.