Quantum Field Theory for Topological Phases of Matter

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.