High Energy Theory Seminar

Quantum field theories can have ordinary global symmetries, as well as generalized higher-form symmetries. 2-group symmetries arise when a generalized 1-form symmetry mixes with ordinary global symmetries. I will discuss theories with continuous 2-group symmetries in four and six spacetime dimensions. Continuous 2-group symmetries are characterized by their current algebras, which allow ordinary currents to fuse into the 2-form current associated with the generalized 1-form symmetry. This leads to unconventional Ward identities and ’t Hooft anomalies for 2-group symmetries that constrain the RG flow. The appropriate classical source for the 2-form current is a 2-form background gauge field, which is subject to non-trivial Green-Schwarz shifts under ordinary background gauge transformations. Theories with 2-group symmetry can be constructed by gauging an ordinary flavor symmetry with suitable mixed 't Hooft anomalies. This leads to many simple and explicit examples, some of which I will describe in detail.