Bullivant, A, Faria Martins, J orcid.org/0000-0001-8113-3646 and Martin, P (2020) Representations of the loop braid group and Aharonov–Bohm like effects in discrete (3+1)-dimensional higher gauge theory. Advances in Theoretical and Mathematical Physics, 23 (7). pp. 1685-1769. ISSN 1095-0753
Abstract
We show that representations of the loop braid group arise from Aharonov–Bohm like effects in finite ‑group -dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call W‑bikoids (welded bikoids). Our main example of W‑bikoids arises from finite ‑groups, realised as crossed modules of groups. Given a W‑bikoid, and hence a groupoid of symmetries, we construct a family of unitary representations of the loop braid group derived from representations of the groupoid algebra. We thus give a candidate for higher Bais’ flux metamorphosis, and hence also a version of a ‘higher quantum group’.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is protected by copyright. All rights reserved. This is an author produced version of an article published in Advances in Theoretical and Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | math-ph; math-ph; hep-th; math.GT; math.MP; math.QA |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number Leverhulme Trust RPG-2018-029 |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Dec 2022 14:35 |
Last Modified: | 24 Nov 2023 19:56 |
Status: | Published |
Publisher: | International Press |
Identification Number: | 10.4310/atmp.2019.v23.n7.a1 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:152198 |