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Cornering Relative Symmetry Theories

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arxiv 2408.12600 v1 pith:HN4GOHNX submitted 2024-08-22 hep-th math.AT

Mirjam Cvetič , Ron Donagi , Jonathan J. Heckman , Max Hübner , Ethan Torres This is my paper · ORCID
classification hep-thmath.AT
keywords bulksymmetrydimensionalstructuretheoriesfieldgappedhigher-dimensional
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abstract

The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated $(d+1)$-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in $D = d+m$ dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this $D$-dimensional bulk system. We present a bottom up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.

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Cited by 5 Pith papers

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

  1. 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.

  2. 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...

  3. 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.

  4. SymTFT actions, Condensable algebras and Categorical anomaly resolutions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.

  5. Symmetry, Symmetry Topological Field Theory and von Neumann Algebra

    hep-th 2025-07 conditional novelty 6.0 of 10

    The symmetric-sector von Neumann algebra of a QFT violates additivity or Haag duality exactly when the Lagrangian algebra of its SymTFT contains operators beyond the identity, with a sharper criterion distinguishing t...

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