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Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
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Tube algebras, excitations statistics and compactification in gauge models of topological phases

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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 07 July 2021

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

  • Alex Bullivant1 &
  • Clement Delcamp  ORCID: orcid.org/0000-0003-2337-57722,3 

Journal of High Energy Physics volume 2021, Article number: 25 (2021) Cite this article

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A preprint version of the article is available at arXiv.

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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Authors and Affiliations

  1. Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.

    Alex Bullivant

  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748, Garching, Germany

    Clement Delcamp

  3. Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, München, Germany

    Clement Delcamp

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  1. Alex Bullivant
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Correspondence to Clement Delcamp.

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Cite this article

Bullivant, A., Delcamp, C. Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases. J. High Energ. Phys. 2021, 25 (2021). https://doi.org/10.1007/JHEP07(2021)025

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  • Received: 26 October 2020

  • Revised: 14 June 2021

  • Accepted: 14 June 2021

  • Published: 07 July 2021

  • DOI: https://doi.org/10.1007/JHEP07(2021)025

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Keywords

  • Topological States of Matter
  • Anyons
  • Gauge Symmetry
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