Symmetry Lost and Found


Shao, S. (2023). Symmetry Lost and Found. Perimeter Institute. https://pirsa.org/23030078


Shao, Shu-Heng. Symmetry Lost and Found. Perimeter Institute, Mar. 28, 2023, https://pirsa.org/23030078


          @misc{ pirsa_PIRSA:23030078,
            doi = {10.48660/23030078},
            url = {https://pirsa.org/23030078},
            author = {Shao, Shu-Heng},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Symmetry Lost and Found},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {mar},
            note = {PIRSA:23030078 see, \url{https://pirsa.org}}

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.

Zoom link:  https://pitp.zoom.us/j/93832561140?pwd=czFFSkVvYS9RbXRjOTJPQVFhL2hGZz09