2024 IHES Summer School: Symmetries and Anomalies: a Modern Take

Summer course at the IHES on:

• Generalized symmetries, Phases of Gauge Theory
• anomalies in condensed matter physics,
• Higher Symmetry in Particle Physics.
• Non-invertible symmetries and their relations to anomalies on the lattice. Kramers-Wannier symmetry in the quantum Ising lattice model and its dynamical consequences. Topological phases protected by non-invertible symmetries. Example: cluster model.
• Generalized, non-invertible symmetries in terms of explicit CFT observable. -> Symmetries are formalized by fusion categories and their gauging.
• String Theory, Symmetries and Anomalies and the Green-Schwartz mechanism.

Lecture notes can be found here