Noninvertible axial symmetry in QED comes full circle

We revisit the possibility of constructing noninvertible topological defects for the axial symmetry of massless quantum electrodynamics (QED), despite its Adler-Bell-Jackiw anomaly. Dressing the defects with a topological quantum field theory with mixed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="double-struck">R</e:mi></e:math>-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 topological field theory 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 <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="double-struck">R</h:mi></h:math> global symmetry. Published by the American Physical Society 2024