Non-invertible symmetries and boundaries in four dimensions

Abstract

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. Moreover, we obtain the ratios of the hemisphere partition functions with these boundary conditions; this result constrains the boundary renormalization group flows under the assumption of the conjectured g-theorem in four dimensions.

18 pages, 19 figures: v2: references and comments added

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• Subsystem Non-Invertible Symmetry Operators and Defects
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Symmetry fractionalization and duality defects in Maxwell theory