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The Non-Invertible Axial Symmetry in QED Comes Full Circle

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arxiv 2405.06596 v1 pith:HYKUJJK4 submitted 2024-05-10 hep-th

Adrien Arbalestrier , Riccardo Argurio , Luigi Tizzano This is my paper
classification hep-th
keywords symmetrydefectsaxialmathbbnon-invertiblerationaltopologicalable
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We revisit the possibility of constructing non-invertible topological defects for the axial symmetry of massless QED, despite its ABJ anomaly. Dressing the defects with a topological quantum field theory with mixed $U(1)$ and $\mathbb{R}$-valued gauge fields, we are able to describe axial rotations of any rational or irrational angle. We confront our results with the existing proposals, in particular those that concern rational angles. We also provide the Symmetry TFT that reproduces the action of all such symmetry defects of QED. Finally, we discuss how similar techniques allow the study of condensation defects for a $\mathbb{R}$ global symmetry.

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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. 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. Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

    hep-th 2025-07 conditional novelty 7.0 of 10

    Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.

  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. 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.

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