Ho Tat Lam (Massachusetts Institute of Technology)

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Ho Tat Lam (Massachusetts Institute of Technology)

November 1, 2022
4:00 PM - 5:00 PM
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Center for Theoretical Physics (Pupin Hall 8th Floor)

Non-invertible Global Symmetries in Nature

We identify 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 Adler-Bell-Jackiw 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. We further apply our construction to the real world QCD in the massless limit, and show that the neutral pion decay can be understood from a matching condition of the non-invertible global symmetry. Generalizing the construction to time-reversal symmetry, we point out that there exists a non-invertible time-reversal symmetry in both the free Maxwell theory and massive QED at every rational theta angle.