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

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