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arXiv · 2401.10165

Anomalies and gauging of U(1) symmetries

Andrea Antinucci·Francesco Benini
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Abstract

We propose the Symmetry 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 non-invertible $\mathbb{Q}/\mathbb{Z}$ chiral symmetry in four dimensions.

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Andrea Antinucci, Francesco Benini. 2024-01-18. Anomalies and gauging of U(1) symmetries. https://doi.org/10.1103/physrevb.111.024110

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