A Fuzzy Sphere Journey in Critical Phenomena
Abstract
This review discusses the recently proposed fuzzy sphere regularization for studying 2 + 1D critical phenomena, particularly three-dimensional (3D) conformal field theory (CFT). The fuzzy sphere scheme not only offers remarkable efficiency in extracting extensive CFT data at low computational cost but also reveals unexpected connections among 3D CFT (critical phenomena), noncommutative geometry, and the quantum Hall effect. We introduce the fundamental ideas of fuzzy sphere regularization, emphasizing its role in demonstrating the state-operator correspondence of 3D CFTs on the geometry. Additionally, we review key developments in this approach across various directions and outline potential future applications.
Fields of Study & Subjects
Noncommutative and Quantum Gravity Theories
Black Holes and Theoretical Physics
Topological Materials and Phenomena
Publication details
- Journal / source
- Annual Review of Condensed Matter Physics
- Publisher
- Annual Reviews
- Volume
- 17
- Issue
- 1
- Pages
- 1–25
- Publication date
- 13 March 2026
- Language
- EN