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Non-Invertible Symmetry Webs

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arxiv 2212.06842 v2 pith:FCO3WRHQ submitted 2022-12-13 hep-th cond-mat.str-elmath.CT

Lakshya Bhardwaj , Lea E. Bottini , Sakura Schafer-Nameki , Apoorv Tiwari This is my paper · ORCID
classification hep-thcond-mat.str-elmath.CT
keywords symmetrynon-invertiblesymmetriesgauginganalysiscategoricalcompletedimensions
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with $G$ 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [1]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups $G$, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.

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Cited by 4 Pith papers

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

  1. Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals

    cond-mat.str-el 2026-07 accept novelty 7.0 of 10

    In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.

  2. 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.

  3. 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...

  4. Unitary Categorical Symmetries

    hep-th 2025-02 conditional novelty 5.0 of 10

    The paper proposes that twisted-sector local operators transform in *-representations of the tube algebra of a higher fusion category symmetry, and classifies these representations using higher S-matrices.

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