Non-invertible topological defects in 4-dimensional $\mathbb {Z}_2$ pure lattice gauge theory

Abstract We explore topological defects in the 4D pure $\mathbb {Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb {Z}_{2}$ center symmetry as well as Kramers–Wannier–Wegner (KWW) duality. We construct the KWW duality topological defects in a similar way to those constructed by Aasen et al. [J. Phys. A 49, 354001 (2016)] for the 2D Ising model. These duality defects turn out to be non-invertible. We also construct 1-form $\mathbb {Z}_{2}$ symmetry defects as well as the junctions between the KWW duality defects and 1-form $\mathbb {Z}_{2}$ center symmetry defects. The crossing relations between these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.