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

Journal of High Energy Physics

Alex Bullivant¹  Clement Delcamp² 

[1] Department of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.;Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748, Garching, Germany;Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, München, Germany;

关键词: Topological States of Matter;    Anyons;    Gauge Symmetry;   

DOI  :  10.1007/JHEP07(2021)025

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY