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

Abstract

We explore topological defects in the 4-dimensional pure ${\mathbb{Z}}_2$ lattice gauge theory. This theory has 1-form ${\mathbb{Z}}_2$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects in the similar way to that constructed by Aasen, Mong, Fendley arXiv:1601.07185 for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. We also construct the 1-form ${\mathbb{Z}}_2$ symmetry defects as well as the junctions among KWW duality defects and 1-form ${\mathbb{Z}}_2$ center symmetry defects. The crossing relations among these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.

Comments: 24 pages, 37 figures, v2: minor correction. v3: references and comments added