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

Understand

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.