Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases

Abstract

We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, the Hamiltonian yields bulk dyonic string-like excitations that terminate at gapped boundaries. Using a tube algebra approach, we classify such excitations and derive the corresponding representation theory. Via a dimensional reduction argument, we relate this tube algebra to that describing (2+1)d boundary point-like excitations at interfaces between two gapped boundaries. Such point-like excitations are well known to be encoded into a bicategory of module categories over the input fusion category. Exploiting this correspondence, we define a bicategory that encodes the string-like excitations ending at gapped boundaries, showing that it is a sub-bicategory of the centre of the input bicategory of group-graded 2-vector spaces. In the process, we explain how gapped boundaries in (3+1)d can be labelled by so-called pseudo-algebra objects over this input bicategory.

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Cited by in corpus (15)

• Dualities in one-dimensional quantum lattice models: topological sectors
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Non-invertible Symmetries and Higher Representation Theory II
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• One dimensional gapped quantum phases and enriched fusion categories
• Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• On tensor network representations of the (3+1)d toric code
• Non-Abelian Fusion, Shrinking and Quantum Dimensions of Abelian Gauge Fluxes
• Crossing with the circle in Dijkgraaf-Witten theory and applications to topological phases of matter
• Boundary topological entanglement entropy in two and three dimensions
• 2-Drinfel'd double symmetry of the 4d Kitaev model
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries