Andrea Antinucci and Francesco Benini propose a Symmetry TFT (Topological Field Theory) for theories with a $U(1)$ symmetry in arbitrary dimensions. The Symmetry TFT describes the structure of the symmetry, its anomalies, and possible topological manipulations. It is constructed as a BF theory of gauge fields for groups $U(1)$ and $\mathbb{R}$, containing a continuum of topological operators. They also propose an operation that produces the Symmetry TFT for the theory obtained by dynamically gauging the $U(1)$ symmetry. The paper discusses various examples, including the Symmetry TFT for the non-invertible $\mathbb{Q}/\mathbb{Z}$ chiral symmetry in four dimensions. The authors provide a Lagrangian description of the Symmetry TFT and explore its properties, such as topological boundary conditions and anomalies. They also discuss the dynamical manipulation of $U(1)$ symmetries, which introduces new degrees of freedom and is not described by topological boundary conditions but by a map between different Symmetry TFTs. The paper concludes with a discussion of the Anomaly Polynomial TFT, which is a $(d+2)$-dimensional TQFT whose $(d+1)$-dimensional topological boundaries correspond to distinct Symmetry TFTs.Andrea Antinucci and Francesco Benini propose a Symmetry TFT (Topological Field Theory) for theories with a $U(1)$ symmetry in arbitrary dimensions. The Symmetry TFT describes the structure of the symmetry, its anomalies, and possible topological manipulations. It is constructed as a BF theory of gauge fields for groups $U(1)$ and $\mathbb{R}$, containing a continuum of topological operators. They also propose an operation that produces the Symmetry TFT for the theory obtained by dynamically gauging the $U(1)$ symmetry. The paper discusses various examples, including the Symmetry TFT for the non-invertible $\mathbb{Q}/\mathbb{Z}$ chiral symmetry in four dimensions. The authors provide a Lagrangian description of the Symmetry TFT and explore its properties, such as topological boundary conditions and anomalies. They also discuss the dynamical manipulation of $U(1)$ symmetries, which introduces new degrees of freedom and is not described by topological boundary conditions but by a map between different Symmetry TFTs. The paper concludes with a discussion of the Anomaly Polynomial TFT, which is a $(d+2)$-dimensional TQFT whose $(d+1)$-dimensional topological boundaries correspond to distinct Symmetry TFTs.