Gapped boundaries and string-like excitations in (3+1)d gauge models of
topological phases
- URL: http://arxiv.org/abs/2006.06536v2
- Date: Wed, 5 May 2021 09:20:01 GMT
- Title: Gapped boundaries and string-like excitations in (3+1)d gauge models of
topological phases
- Authors: Alex Bullivant, Clement Delcamp
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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