Noninvertible symmetries and boundaries in four dimensions

We study quantum field theories with boundaries by utilizing noninvertible symmetries. We consider three kinds of boundary conditions of the four dimensional Z2 lattice gauge theory at the critical point as examples. The weights of the elements on the boundary are 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 are topological. Moreover, we obtain the ratios of the hemisphere partition functions with these boundary conditions; this result constrains the boundary renormalization group flows.

Automated summary

In this study, quantum field theories with boundaries are investigated using noninvertible symmetries. The examples of the four-dimensional Z2 lattice gauge theory at the critical point are considered with three different boundary conditions. By determining the weights of the elements on the boundary, the boundary conditions are shown to be related through Kramers-Wannier-Wegner (KWW) duality, with the requirement that the KWW duality defects ending on the boundary possess topological properties. Furthermore, the ratios of the hemisphere partition functions with these boundary conditions are obtained, providing constraints on the boundary renormalization group flows.