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Schweigert, ChristophORCID iD iconorcid.org/0000-0003-1342-6230
Publications (2 of 2) Show all publications
Fuchs, J., Priel, J., Schweigert, C. & Valentino, A. (2015). On the Brauer Groups of Symmetries of Abelian Dijkgraaf-Witten Theories. Communications in Mathematical Physics, 339(2), 385-405
Open this publication in new window or tab >>On the Brauer Groups of Symmetries of Abelian Dijkgraaf-Witten Theories
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
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.

National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-41597 (URN)10.1007/s00220-015-2420-y (DOI)000358130400003 ()
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Fuchs, J. & Schweigert, C. (2015). Surface defects and symmetries. In: XXXTH International Colloquium on Group Theoretical Methods in Physics (ICGTMP) (GROUP30): . Paper presented at 30th International Colloquium on Group Theoretical Methods in Physics (ICGTMP), Jul 14-18, 2014, Ghent, Belgium. Institute of Physics (IOP), Article ID 012002.
Open this publication in new window or tab >>Surface defects and symmetries
2015 (English)In: XXXTH International Colloquium on Group Theoretical Methods in Physics (ICGTMP) (GROUP30), Institute of Physics (IOP), 2015, article id 012002Conference paper, Published paper (Refereed)
Abstract [en]

In quantum field theory, defects of various codimensions are natural ingredients and carry a lot of interesting information. In this contribution we concentrate on topological quantum field theories in three dimensions, with a particular focus on Dijkgraaf-Witten theories with abelian gauge group. Surface defects in Dijkgraaf-Witten theories have applications in solid state physics, topological quantum computing and conformal field theory. We explain that symmetries in these topological field theories are naturally defined in terms of invertible topological surface defects and are thus Brauer-Picard groups.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2015
Series
Journal of Physics Conference Series, ISSN 1742-6588 ; 597
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-41650 (URN)10.1088/1742-6596/597/1/012002 (DOI)000354929400002 ()
Conference
30th International Colloquium on Group Theoretical Methods in Physics (ICGTMP), Jul 14-18, 2014, Ghent, Belgium
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2016-05-31Bibliographically approved
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1342-6230

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