On anomalies and gauging of U(1) non-invertible symmetries in 4d QED

Understand

In this work we propose a way to promote the anomalous axial U(1) transformations to exact non-invertible U(1) symmetries.

• We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field.
• We show that as part of the gauging procedure, certain constraints are imposed to make the gauging consistent.
• The constraints emerge naturally from the form of the non-invertible U(1) conserved current.