We identify infinitely many new 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 ABJ 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 over TQFT coefficients. 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 neutral pion decay can be understood from a matching condition of the non-invertible global symmetry.

Host: Bianka Mecaj, Yuan Xin, Petar Tadic

# High Energy Particle Theory Seminar: New Global Symmetries in Nature

Event time:

Tuesday, September 27, 2022 - 4:00pm to 5:00pm

Location:

Sloane Physics Laboratory (SPL), Room 51

217 Prospect Street

New Haven, CT
06511
Event description:

Contact:

(see "Description" above)