Non-invertible symmetries and boundaries in four dimensions

Understand

We study quantum field theories with boundary by utilizing non-invertible symmetries.

• We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples.
• The weights of the elements on the boundary is determined so that these boundary conditions are related by the Kramers-Wannier-Wegner (KWW) duality.
• In other words, it is required that the KWW duality defects ending on the boundary is topological.