Generalized Global Symmetries

Abstract:  Symmetry has proven to be of fundamental importance for describing Nature. I will discuss recent developments in various generalizations of global symmetries and their applications in quantum field theory, condensed matter physics, mathematics, and quantum gravity.  These new global symmetries exist in a variety of quantum systems, ranging from the Ising model, to topological phases of anyons and fractons, and even to the Standard Model. In the case of fractons and related exotic lattice models in condensed matter physics, the generalized global symmetry results in a surprising UV/IR mixing. More recently, a new global symmetry was discovered in QCD, which provides an alternative explanation for the neutral pion decay in the real world.