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.
’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symm etry breaking , NATO Sci.Ser.B 59 (1980) 135
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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.