"A Holographic View on Symmetry”

The aim of this lecture is to introduce, from an elementary bottom-up approach, a modern viewpoint on global finite symmetries in QFT_d, utilizing a (d+1)-dimensional Topological Quantum Field Theory (TQFT). To do so, in the first part I will elucidate several concepts on generalized global symmetries, clarifying that a subset of them can be understood in very elementary way precisely as ordinary global symmetries found in textbooks. I will briefly explain why the most general notion of (non-)symmetries is described mathematically by some kind of higher fusion category. In the second part, I will explain the holographic viewpoint, which enables the study of these complicated algebraic structures in terms of often simpler TQFTs in one dimension higher. If time permits I will describe how anomalies of generalized symmetries are encoded in this framework and how they can be employed to constraint the dynamics