The Basics of Non-Invertible Symmetries and Dualities - Lecture II

Explore advanced concepts in theoretical physics through this comprehensive lecture that delves into the fundamental principles of non-invertible symmetries and their relationship to dualities in quantum field theory. Learn how these mathematical structures differ from traditional invertible symmetries and discover their applications in understanding phase transitions, topological phases of matter, and quantum many-body systems. Examine specific examples of non-invertible symmetry operations, their algebraic properties, and how they manifest in various physical models including lattice systems and continuum field theories. Investigate the deep connections between non-invertible symmetries and dualities such as Kramers-Wannier duality, understanding how these relationships provide new insights into the classification and behavior of quantum phases. Master the mathematical framework needed to work with fusion categories and their physical interpretations, while gaining practical skills in identifying and analyzing non-invertible symmetries in concrete physical systems.