@article{TEXTUAL,
      recid = {11391},
      author = {Córdova, Clay and Ohmori, Kantaro},
      title = {Noninvertible Chiral Symmetry and Exponential Hierarchies},
      journal = {Physical Review X},
      address = {2023-03-08},
      number = {TEXTUAL},
      abstract = {We elucidate the fate of classical symmetries which suffer  from Abelian Adler-Bell-Jackiw anomalies. Instead of being  completely destroyed, these symmetries survive as  noninvertible topological global symmetry defects with  world volume anyon degrees of freedom that couple to the  bulk through a magnetic 1-form global symmetry as in the  fractional Hall effect. These noninvertible 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). When the associated bulk  magnetic 1-form symmetry is broken by the propagation of  dynamical magnetic monopoles, the selection rules of the  noninvertible chiral symmetry defects are violated  nonperturbatively. This leads to technically natural  exponential hierarchies in axion potentials and fermion  masses. },
      url = {http://knowledge.uchicago.edu/record/11391},
}