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Anomalies and gauging of U(1) symmetries

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arxiv 2401.10165 v4 pith:PFOIZRK4 submitted 2024-01-18 hep-th

Andrea Antinucci , Francesco Benini This is my paper
classification hep-th
keywords symmetrymathbbanomaliesgaugingproposetheorytopologicalarbitrary
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies

    hep-th 2026-07 accept novelty 7.0 of 10

    An order-five Sp(4,Z) duality acts projectively on 3d U(1)^2 theories, and its hierarchy operations generate candidate bilayer quantum Hall states at 3/8+3/8 and 5/12+5/12.

  2. Symmetry extension by condensation defects II: general dimensions and higher-groups

    hep-th 2026-07 conditional novelty 7.0 of 10

    Gauging A×B under a cubic mixed anomaly extends C (n=1) or folds C into a higher-group (n≥2), with the new factor generated by condensation defects and detected via triple-linking.

  3. Generalized Families of QFTs

    hep-th 2026-02 unverdicted novelty 7.0 of 10

    Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.

  4. The Line, the Strip and the Duality Defect

    hep-th 2026-02 unverdicted novelty 7.0 of 10

    The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.

  5. Symmetry TFTs for Continuous Spacetime Symmetries

    hep-th 2025-09 conditional novelty 7.0 of 10

    Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.

  6. Disjoint additivity and local quantum physics

    hep-th 2025-09 conditional novelty 7.0 of 10

    Local quantum systems should obey disjoint additivity plus Haag duality, a combination that survives higher-form symmetries and fails for known nonlocal constructions.

  7. Notes on (-2)-form symmetries

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...

  8. Continuous symmetries and charge measurement of boundary operators in holography

    hep-th 2026-02 conditional novelty 6.0 of 10

    Continuous symmetry operators in holography are U-shaped hanging brane bound states (D5-KK in Type IIB, M5-KK in M-theory) whose worldvolume couplings reproduce the Gauss-law symmetry operators and measure charges of ...

  9. SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking

    hep-th 2025-09 conditional novelty 6.0 of 10

    Continuous-symmetry SymTFTs are extended to non-linear coset realizations and to spontaneous breaking using boundary and corner constructions, recovering CCWZ actions and SSB Ward identities.

  10. Topological Holography for Mixed-State Phases and Phase Transitions

    cond-mat.str-el 2025-07 conditional novelty 6.0 of 10

    Mixed-state phases of (1+1)D systems with finite group symmetry are classified by condensable algebras in the doubled topological order Z(Vec_{GxG}) subject to Hermiticity and positivity constraints.

  11. R-symmetries, anomalies and non-invertible defects from non-BPS branes

    hep-th 2025-06 conditional novelty 6.0 of 10

    The U(1)_R symmetry operator of the Klebanov-Witten theory is realized by a non-BPS KK monopole, whose worldvolume action matches the SymTh operator and anomaly coefficients.

  12. Linking defects via AdS/CFT holography

    hep-th 2026-07 reject novelty 5.0 of 10

    A hanging D5/anti-D5 pair in a deformed AdS5 x S5 background is proposed as the topological defect that measures the U(1) charge of determinant operators.

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