From Fusion Categories to Anyon Theories - Lecture 2

Explore the mathematical foundations connecting fusion categories to anyon theories in this advanced physics lecture delivered by Julien Vidal at the International Centre for Theoretical Sciences. Delve into the sophisticated mathematical framework that bridges abstract category theory with the physical properties of anyons, exotic particles that exist in two-dimensional systems and exhibit neither bosonic nor fermionic statistics. Learn how fusion categories provide the mathematical language to describe the braiding and fusion properties of anyons, which are crucial for understanding topological quantum phases of matter and their potential applications in quantum computing. Examine the systematic approach to constructing anyon theories from categorical data, including the role of fusion rules, braiding statistics, and modular transformations. Discover how these mathematical structures encode the essential physics of topological phases, from fractional quantum Hall states to spin liquids, and understand their implications for quantum error correction and topological quantum computation. This lecture forms part of a comprehensive program on generalized symmetries and anomalies in quantum phases of matter, providing essential theoretical tools for researchers working on topological quantum matter and quantum many-body systems.