Noninvertible symmetries and boundaries in four dimensions

Abstract

We study quantum field theories with boundaries by utilizing noninvertible 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 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.