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

Understand

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.