Seminar held by Andrea Antinucci

HEP-Theory Group, Milano-Bicocca, talks

Title: Anomalies and gauging of U(1) symmetries

It is well known that d-dimensional QFTs can require an almost trivial d+1-dimensional bulk to cancel their anomalies by inflow. For finite symmetries, this picture has recently been "upgraded" to the so-called Symmetry TFT: the bulk is promoted to a non-trivial TQFT, capturing simultaneously the symmetries and anomalies of various boundary QFTs related by topological manipulation. This tool has proven to be incredibly effective and has been extended to various types of generalized symmetries, including non-invertible symmetries, but has been restricted to finite symmetries. In this talk, I will explain how to go beyond this limitation and include continuous symmetries. This requires studying certain new TQFTs with a continuum of operators, which are interesting in their own right. Additionally, a precise map is found between pairs of these TQFTs, corresponding to gauging the continuous symmetry. Finally, I will propose the existence of a d+2-dimensional TQFT whose boundaries are the Symmetry TFTs describing the symmetries of d-dimensional QFTs related by gauging. Along the way, I will discuss various examples, including the Symmetry TFT for the non-invertible Q/Z chiral symmetry of 4d QED