Quantum Matter in Mathematics and Physics

Title: Non-invertible Symmetries in Nature

Abstract: 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/2205.05086 and https://arxiv.org/abs/2208.04331.