When ℤ2 one-form symmetry leads to non-invertible axial symmetries

A bstract We study non-abelian gauge theories with fermions in a representation such that the surviving electric 1-form symmetry is ℤ 2. This includes SU (N) gauge theories with matter in the (anti) symmetric and N even, and USp (2 N) with a Weyl fermion in the adjoint, i. e. N N = 1 SYM. We study the mixed ’t Hooft anomaly between the discrete axial symmetry and the 1-form symmetry and show that when it is non-trivial, it leads to non-invertible symmetries upon gauging the ℤ 2. The TQFT dressing the non-invertible symmetry defects is universal to all the cases we study, namely it is always a U (1) 2 CS theory coupled to the ℤ 2 2-form gauge field. We uncover a pattern where the presence or not of non-invertible defects depends on the rank of the gauge group.