Non-invertible Global Symmetries in the Standard Model

          @misc{ pirsa_PIRSA:22060010,
            doi = {10.48660/22060010},
            url = {https://pirsa.org/22060010},
            author = {Shao, Shu-Heng},
            keywords = {Mathematical physics},
            language = {en},
            title = {Non-invertible Global Symmetries in the Standard Model},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060010 see, \url{https://pirsa.org}}
          }
          

Abstract

We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the axial symmetry because of the ABJ anomaly, for every rational angle, we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic U(1) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra over TQFT coefficients. These non-invertible symmetries lead to selection rules, which are consistent with the scattering amplitudes in QED. We further generalize our construction to QCD, and show that the neutral pion decay can be understood from a matching condition of the non-invertible global symmetry.