Modave lecture notes: Field exploration in phases of matter

A new look has been given to symmetries in quantum field theory in the last ten years. Generalized symmetries broadened our vision of their role in constraining the renormalization group flow. Together with the knowledge of their anomalies, they can be used to classify phases of matter that fall outside the scope of Landau’s paradigm with ordinary symmetries. Examples include superfluids on thin layers, deconfined phases of gauge theories, and field theories with topological order. These lectures will introduce these notions and work out examples of quantum field theories that exhibit such phases.