CMSA Quantum Matter in Mathematics and Physics: Non-invertible Symmetries in Nature
SEMINARS, CMSA EVENTS
Speaker:
Yichul Choi - SUNY Stony Brook
In this talk, I will discuss non-invertible symmetries in familiar 3+1d quantum field theories describing our Nature. In massless QED, the classical U(1) axial symmetry is not completely broken by the ABJ anomaly. Instead, it turns into a discrete, non-invertible symmetry. The non-invertible symmetry operator is obtained by dressing the naïve U(1) axial symmetry operator with a fractional quantum Hall state. We also find a similar non-invertible symmetry in the massless limit of QCD, which provides an alternative explanation for the neutral pion decay. In the latter part of the talk, I will discuss non-invertible time-reversal symmetries in 3+1d gauge theories. In particular, I will show that in free Maxwell theory, there exists a non-invertible time-reversal symmetry at every rational value of the theta angle.
Based on https://arxiv.org/abs/2205.
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