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Exploring Non-Invertible Symmetries in Free Theories

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arxiv 2209.11166 v2 pith:PIRCSICG submitted 2022-09-22 hep-th

classification hep-th
keywords defectdefectsdimensionsfreetheorytopologicalactionangle
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one) topological defects by specifying a map between gauge-invariant operators from one side of the defect and such operators on the other side. In this work, we apply such construction to Maxwell theory in four dimensions and to the free compact scalar theory in two dimensions. In the case of Maxwell theory, we show that a topological defect that mixes the field strength $F$ and its Hodge dual $\star F$ can be at most an $SO(2)$ rotation. For rational values of the bulk coupling and the $\theta$-angle we find an explicit defect Lagrangian that realizes values of the $SO(2)$ angle $\varphi$ such that $\cos \varphi$ is also rational. We further determine the action of such defects on Wilson and 't Hooft lines and show that they are in general non-invertible. We repeat the analysis for the free compact scalar $\phi$ in two dimensions. In this case we find only four discrete maps: the trivial one, a $Z_2$ map $d\phi \rightarrow -d\phi$, a $\mathcal{T}$-duality-like map $d\phi \rightarrow i \star d\phi$, and the product of the last two.

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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

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    hep-lat 2026-07 conditional novelty 7.0 of 10

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  3. The Line, the Strip and the Duality Defect

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    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.

  4. 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...

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