Presented By: Leinweber Center for Theoretical Physics
HET Seminar | What's Done Cannot Be Undone: Non-Invertible Symmetries
Shu-Heng Shao (Stony Brook)
In massless QED, we find that the classical U(1) chiral symmetry is not completely broken by the Adler-Bell-Jackiw anomaly. Rather, it is resurrected as a generalized global symmetry labeled by the rational numbers. Intuitively, this new global symmetry in QED is a composition of the naive axial rotation and a fractional quantum Hall state. The conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra. We further generalize our construction to QCD, and show that the neutral pion decay can be derived from a matching condition of the non-invertible global symmetry.
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