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On the Brauer Groups of Symmetries of Abelian Dijkgraaf-Witten Theories
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-4081-6234
Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany..
Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany..ORCID iD: 0000-0003-1342-6230
Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany..
2015 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 339, no 2, p. 385-405Article in journal (Refereed) Published
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Abstract [en]

Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group A, and with vanishing 3-cocycle, is generated by group automorphisms of A, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of A-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category and braided auto-equivalences of its Drinfeld center . The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.

Place, publisher, year, edition, pages
2015. Vol. 339, no 2, p. 385-405
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Physical Sciences
Research subject
Physics
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URN: urn:nbn:se:kau:diva-41597DOI: 10.1007/s00220-015-2420-yISI: 000358130400003OAI: oai:DiVA.org:kau-41597DiVA, id: diva2:918686
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

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Fuchs, JürgenSchweigert, Christoph

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