Noninvertible symmetries and boundaries in four dimensions
Masataka Koide, Yuta Nagoya, Satoshi Yamaguchi
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.
Topics & Concepts
Homogeneous spaceBoundary (topology)PhysicsDuality (order theory)Boundary value problemBoundary conformal field theoryLattice (music)Mathematical physicsQuantum field theoryGauge theoryQuantum mechanicsMathematicsMathematical analysisMixed boundary conditionPure mathematicsRobin boundary conditionGeometryAcousticsBlack Holes and Theoretical PhysicsQuantum many-body systemsPhysics of Superconductivity and Magnetism