• Corpus ID: 248693363

Non-invertible Global Symmetries in the Standard Model

@inproceedings{Choi2022NoninvertibleGS,
  title={Non-invertible Global Symmetries in the Standard Model},
  author={Yichul Choi and Ho Tat Lam and Shu-Heng Shao},
  year={2022}
}

• Yichul Choi, Ho Tat Lam, S. Shao
• Published 10 May 2022
• Mathematics, Physics

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 U (1) A axial symmetry because of the ABJ anomaly, for every rational angle 2 πp/N , we construct a conserved and gauge-invariant topological symmetry operator. Intu-itively, 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. They act invertibly on all local operators as axial rotations, but non-invertibly on the ’t Hooft lines. 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 coupling π 0 F ∧ F in the effective pion Lagrangian is necessary to match these non-invertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.