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Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A simple argument
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abstract
Employing the modified Villain lattice formulation of the axion quantum electrodynamics, we present an alternative and much simpler derivation of the conclusion of~Ref.~\cite{Honda:2024sdz} that the sweep of the axial $U(1)$ non-invertible symmetry operator over the (non-genuine) gauge invariant 't~Hooft line operator with an integer magnetic charge does not leave any effect. The point is that such a 't~Hooft line can be represented by a boundary of a (non-topological) defect that is invariant under the axial transformation on the axion field.
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Cited by 1 Pith paper
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Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry
A lattice construction of axion QED with gauge-invariant 't Hooft loops is given, and the non-invertible chiral symmetry is shown to act non-invertibly on them, either vanishing or attaching a field-strength surface.
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