Anomalies and gauging of U (1) symmetries

We propose the Symmetry topological field theory (TFT) for theories with a U (1) symmetry in arbitrary dimension. The Symmetry TFT describes the structure of the symmetry, its anomalies, and the possible topological manipulations. It is constructed as a BF theory of gauge fields for groups U (1) and R, and contains a continuum of topological operators. We also propose an operation that produces the Symmetry TFT for the theory obtained by dynamically gauging the U (1) symmetry. We discuss many examples. As an interesting outcome, we obtain the Symmetry TFT for the noninvertible Q/Z chiral symmetry in four dimensions.