USEPT at Princeton University

by Weiguang Cao

It is a great honor to attend the University-wide Student Exchange Program (USEPT) and study in Princeton University. Also, thanks to the financial support of Ito Foundation U.S.A., Hsun Kwei & Aiko Takizawa Chou, and Friends of UTokyo, Inc. to make this trip possible. 

Study & Research:

Princeton University is famous for its strong faculties and scholars on Physics. As a student in physics major, this exchange give me a great opportunity to have discussions with these profound professors and researchers. During my exchange in Princeton University, I am supervised by Professor Shinsei Ryu, a distinguished professor in theoretical physics and also an alumni of the University of Tokyo. With professor Ryu, I am investigating exotic phases of matter with newly established symmetries. 

Symmetry, often celebrated in art and design, holds a pivotal role in describing the fundamental laws governing our world, spanning from classical Newtonian mechanics to the Standard Model in quantum physics. However, recent developments have revealed that our universe possesses more profound symmetries than previously anticipated. The concept of global symmetry has undergone a remarkable generalization in various directions.

My current research interest lies in the interface of non-invertible symmetry and exotic symmetry. Non-invertible symmetry extends the algebraic relations between symmetry operators from groups to categories. In this framework, symmetry operators are not required to have an inverse, meaning that symmetry transformations cannot always be undone. On the other hand, exotic symmetry permits the existence of quasi-particles with restricted mobility, unable to move freely due to the constraints of this symmetry.

My primary objective is to establish the most comprehensive definition of global symmetry. To achieve this goal, I will explore new symmetries and expand the boundaries of generalization. Notably, I have introduced a novel concept known as subsystem non-invertible symmetry by constructing non-invertible symmetry with a unique exotic symmetry, subsystem symmetry. This new non-invertible symmetry exhibits a t’ Hooft anomaly, which provides information about the theory’s ground state without requiring additional calculations. My research includes exploring the duality with subsystem symmetry. Duality gives two (or more) different descriptions of the same theory and allows us to study the theory from multiple perspectives. Duality defect is one way to construct non-invertible symmetry. My work on subsystem Jordan-Wigner duality provides an explicit mapping from a bosonic theory to a fermionic theory, thereby leading to more examples of fermionic models with subsystem symmetry. My work on subsystem Kramers-Wannier duality, which relates high temperature (weak coupling) to low temperature (strong coupling) of the theory in classical (quantum) models, results in the new subsystem non-invertivle symmetry.

As a continuation of my research, I will investigate more duality structures in conjunction with other exotic symmetries, such as fractal symmetry, where the symmetry transformation acts on fractal submanifold and the quasi-particles exhibit no mobility. This will lead to new exotic non-invertible symmetries, which will enrich our understanding of the web of generalization.

Facilities & Activities:

Princeton University is also near the Institute of Advanced Study (IAS), which is the dream place to conduct theoretical physics. I often attended the workshops and seminars in IAS. In July, I attended the summer school: Prospects in Theoretical Physics 2023, during which the Nobel laureate David Gross gave a public talk. In September, I also gave a seminar talk in the IAS CMT/QFT Group Meeting about my research.

Princeton University has a a great campus with beautiful architecture and active student associations. As a exchange graduate student, I received invitations of student’s events every week. I also helped the staffs of the University of Tokyo in the Princeton Study Abroad Fair as a volunteer.