Non-Invertible Chiral Symmetry
Clay Córdova (University of Chicago)

We elucidate the fate of classical symmetries which suffer from abelian
Adler-Bell-Jackiw anomalies. Instead of being completely destroyed,
these symmetries survive as non-invertible topological global symmetry
defects with worldvolume anyon degrees of freedom that couple to the
bulk through a magnetic one-form global symmetry as in the fractional
hall effect. These non-invertible chiral symmetries imply selection
rules on correlation functions and arise in familiar models of massless
quantum electrodynamics and models of axions (as well as their non-
abelian generalizations)