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 $\mathbb{R}$, 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 $\mathbb{Q}/\mathbb{Z}$ chiral symmetry in four dimensions.

• MD
  Ministero dell'Università e della Ricerca

  Awards: R20E8NR3HX, 2022NY2MXY
• HE
  H2020 European Research Council

  Award: 864583