Generalized Global Symmetries

<!--HTML--><p>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, and quantum gravity.&nbsp; These generalized global symmetries exist ubiquitously in familiar quantum systems, including the Ising model, Maxwell theory, lattice gauge theories, and Yang-Mills theories. They also feature in more novel topological phases of quantum matter such as fractons.&nbsp; These new symmetries can have generalized anomalies, which lead to&nbsp;nontrivial dynamical consequences on renormalization group flows and analytic constraints on the phase diagram of gauge theories.&nbsp; In the case of fractons and related exotic lattice models in condensed matter theory, the generalized global symmetry results in a surprising UV/IR mixing.</p>