Noninvertible chiral symmetry and axions under electromagnetic duality

We study the implications of noninvertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>L</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:mo>,</a:mo> <a:mi mathvariant="double-struck">Z</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> duality. This is done by deriving the Adler-Bell-Jackiw anomaly of massless QED in the dual frame that is used to explicitly construct the symmetry defect operator as well as the conserved two-form symmetry current. As expected, the noninvertible chiral symmetry is covariant under the duality transformation. This has implications for understanding the nature of kinetic and topological terms in the dual frame and for axion electrodynamics. In particular, we show that to generate an axion potential from a dyon loop, the one-form magnetic symmetry must be explicitly broken by a mutually nonlocal charged state with nonzero pairwise helicity.