Symmetry Lost and Found

PIRSA ID: 23030078
Event Type: Seminar
Domaine(s) scientifique(s) :
Quantum Fields and Strings
Date de fin :
  • Shu-Heng Shao, Stony Brook University

In massless QED, we find that the classical U(1) axial 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. Finally, we find a non-invertible Gauss law in axion-Maxwell theory.

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