On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
| Autor: | Fuchs, Jürgen, Priel, Jan, Schweigert, Christoph, Valentino, Alessandro |
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| Rok vydání: | 2014 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00220-015-2420-y |
| Popis: | 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. Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and references added. v3: Typos corrected |
| Databáze: | arXiv |
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