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

• Main Authors: Alex Bullivant, Clement Delcamp
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Journal of High Energy Physics
• Subjects: Topological States of Matter; Anyons; Gauge Symmetry
• Online Access: https://doi.org/10.1007/JHEP07(2021)025

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.