Title: Non-invertible Gauss Law and Axions
Speaker: Yichul Choi (Stony Brook University)
Abstract: In this talk, we discuss non-invertible 1-form symmetries in the 3+1d axion-Maxwell theory. Naively, the presence of the axion-photon coupling term explicitly breaks the electric 1-form symmetry, hence making the Gauss law anomalous. However, we show that an infinite discrete subset of symmetry operators survives as non-invertible symmetries. These non-invertible 1-form symmetries act invertibly on the Wilson lines in the same way as the ordinary electric 1-form symmetry, but act non-invertibly on monopoles and axion strings. Also, they mix with other higher-form symmetries of the theory in an intricate way. As an application, we show that in a U(1) gauge theory, monopoles must be heavier than electrons if the theory is described by the axion-Maxwell theory at low energy.