The progress in our understanding of symmetries in QFT has led to the proposal that the complete information on a symmetry structure is encoded in a TQFT in one dimension higher, known as the Symmetry TFT. This picture is well understood for finite symmetries, and I will explain the extension to continuous symmetries in the first part of the talk, based on a paper with F. Benini. This extension requires studying new TQFTs with a non-compact spectrum of operators. Like for finite symmetries, these TQFTs capture anomalies and topological manipulations via their topological boundary conditions. The main new ingredient for continuous symmetries is dynamical gauging, which is described by maps between different TQFTs. I will use this to derive the Symmetry TFT for the non-invertible chiral symmetry of QED. Moreover, the various TQFTs related by dynamical gauging arise as different boundary conditions of a unique TQFT in two dimensions higher. In the second part of the talk, based on work in progress with F. Benini and G. Rizi, I will use these tools to derive some new connections between the Symmetry TFTs and the universal EFTs describing the spontaneous symmetry breaking of any (generalized) global symmetry.
