Non-invertible topological defects in 4-dimensional Z2 pure lattice gauge theory

We explore topological defects in the 4D pure Z(2) lattice gauge theory. This theory has 1-form 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. [I Phys. A 49, 354001 (2016)] for the 2D Ising model. These duality defects turn out to be non-invertible. We also construct 1-form Z(2) symmetry defects as well as the junctions between the KWW duality defects and 1-form 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.

Automated summary

We explore topological defects in the 4D pure Z(2) lattice gauge theory, including the topological defects of KWW duality and 1-form Z(2) center symmetry, and derive the crossing relations between them.