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Lower-Form Symmetries

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arxiv 2211.04461 v1 pith:COTKUUY5 submitted 2022-11-08 hep-th

Lower-Form Symmetries

Thomas Vandermeulen This is my paper
classification hep-th
keywords formsymmetrygaugingsymmetriestheorydirectfieldtheories
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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When gauging a $(d-1)$-form symmetry in $d$ spacetime dimensions, one formally expects the gauged theory to carry a dual $-1$-form symmetry. This work focuses on the study of such symmetries, in particular via the spacetime-filling topological operators that implement them, in two-dimensional field theory (with an eye towards general quantum field theory). As theories with $(d-1)$-form symmetries are known to be equivalent to direct sums of local theories, we review how gauging a $(d-1)$-form symmetry projects onto a single component in this sum, and explain how gauging the resulting $-1$-form symmetry restores the direct sum.

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Cited by 4 Pith papers

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

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

    hep-th 2026-07 conditional novelty 7.0

    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.

  2. Generalized Families of QFTs

    hep-th 2026-02 unverdicted novelty 7.0

    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.

  3. Notes on (-2)-form symmetries

    hep-th 2026-06 conditional novelty 6.0

    (-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.

  4. Notes on (-2)-form symmetries

    hep-th 2026-06 unverdicted novelty 5.0

    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...