  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.
